Photomask, productyion method of the same, pattern forming method using the photomask

ABSTRACT

A mask pattern  40  including a light-shielding portion  41  constituted by a light-shielding film made of a chromium film or the like and phase shifters  42  and  43  is formed on a transparent substrate  30.  The phase shifters  42  and  43  generate a phase difference of 180 degrees with respect to exposure light between the phase shifters and the transparent substrate  30.  A first light intensity generated in a light-shielded image formation region corresponding to the mask pattern  40  on an exposed material by the exposure light transmitted through the phase shifters  42  and  43  is not more than four times a second light intensity generated in the light-shielded image formation region by the exposure light that is transmitted through the periphery of the mask pattern  40  on the transparent substrate  30  and goes into the back side of the mask pattern  40.

TECHNICAL FIELD

[0001] The present invention relates to a photomask for pattern exposureused for producing a semiconductor device or a liquid crystal displayapparatus, a method for forming the same and a method for formingpatterns using the photomask. The present invention further relates to amethod for designing a mask pattern.

BACKGROUND ART

[0002] In recent years, as a result of development of miniaturization oflarge-scale integrated circuit devices (hereinafter, referred to as“LSI”) that are realized by using semiconductors, a discrepancy in theshape or the size between a mask pattern and a processed pattern (e.g.,a resist pattern formed by pattern transfer onto a resist film) cannotbe ignored any more in a lithography process, which is one process forLSI production.

[0003] The miniaturization of a pattern size of LSIs has developed tothe extent that the limit of resolution defined by the wavelength ofexposure light or the numerical aperture of a projecting optical systemof an exposure apparatus has been reached, so that production marginregarding the yield in LSI production, for example, a depth of focus,has been significantly reduced.

[0004] When forming a pattern having a desired shape as a resist patternon a wafer by a conventional pattern forming method, a light-shieldingpattern, that is, a mask pattern, having a desired shape is formed on atransparent substrate with a light-shielding film made of a metal suchas chromium, and then the wafer coated with a resist film is exposed tolight, using the transparent substrate on which the mask pattern isformed as a mask. In this exposure process, a light intensitydistribution having a shape similar to the mask pattern formed of thelight-shielding film is projected into the resist film. Furthermore,this light intensity distribution generates stored energy in the resistfilm, and a reaction is effected in a portion of the resist film inwhich the stored energy becomes larger than a predetermined magnitude.Herein, the light intensity corresponding to the stored energy having amagnitude that causes a reaction in the resist film is referred to as“critical intensity”.

[0005] In the case where, for example, a positive resist is used as theresist film, the portion having a light intensity more than the criticalintensity in the resist film is removed by developing the resist film.Thus, a resist pattern having a desired shape can be formed by matchinga distribution shape or dimension of the critical intensity value in thelight intensity distribution occurring in an exposed material by patternexposure to a desired pattern.

[0006] FIGS. 53(a) to 53(d) are cross-sectional views showing processesin a conventional method for forming a pattern.

[0007] First, as shown in FIG. 53(a), a film 801 to be processed made ofa metal film or an insulating film is formed on a substrate 800, andthen as shown in FIG. 53(b), a positive resist film 802 is formed on thefilm 801 to be processed. Thereafter, as shown in FIG. 53(c), the resistfilm 802 is irradiated with exposure light 820 via a photomask 810including a transparent substrate 811 and a mask pattern 812 having apredetermined shape made of a chromium film or the like formed thereon.Thus, a portion corresponding to the mask pattern 812 in the resist film802 (a portion having a light intensity of not more than the criticalintensity) becomes a non-exposed portion 802 a, and other portions(portions having a light intensity of the critical intensity or more)become an exposed portion 802 b. Thereafter, as shown in FIG. 53(d), aresist pattern 803 constituted by the non-exposed portion 802 a isformed by developing the resist film 802.

[0008] In the method for forming a pattern as described above, ingeneral, a reduced size projection exposure apparatus is used. Thereduced size projection exposure apparatus performs pattern formationby, for example, subjecting a resist film made of a photosensitive resinformed on a wafer serving as a substrate to reduced size projectionexposure, using a photomask, which is a transparent substrate on which amask pattern magnified to a size of several times larger than the sizeof a resist pattern to be formed. In the description of thisspecification, the following letters are defined as follows:

[0009] NA: the numerical aperture of a projecting optical system of anexposure apparatus (e.g., 0.6);

[0010] λ: the wavelength of exposure light (light source) (e.g., 0.193μm)

[0011] M: the magnification factor of the exposure apparatus (theinverse number of the reduction ratio, e.g., 4 or 5); and

[0012] L: the pattern size (designed value) on a wafer (an exposedmaterial).

[0013] For example, in the case where a desired pattern size (designedvalue) on a wafer is 0.1 μm, L=0.1 μm, and in this case, the maskpattern size on a photomask used in an exposure apparatus having amagnification factor M=4 is 0.1×4=0.4 μm. For simplification of thefollowing description, when indicating a mask pattern size on aphotomask, a designed value on a wafer, that is, a calculated value (avalue obtained as a result of multiplication by a reduction ratio) isused, unless otherwise specified.

[0014] As well known, in the case where light is shielded by a patternhaving a size of not more than a half of the wavelength of the light,the contrast of a light-shielded image is reduced by diffraction oflight. This means that when the mask pattern is smaller than a half of avalue defined by M×λ/NA, where λ is the wavelength of exposure light ina reduction projection optical system, M is the magnification factor,and NA is the numerical aperture, then the contrast of an imagetransferred by the mask pattern, that is, a light-shielded image isdegraded.

[0015]FIG. 54(a) shows an example of a layout of the mask pattern 812 onthe photomask 810 used in the exposure process shown in FIG. 53(c). Asshown in FIG. 54(a), the mask pattern 812 has a size (actual size) of0.26×M [μm] (M: the magnification factor of an exposure apparatus usedin the exposure process).

[0016]FIG. 54(b) shows the simulation results of a light intensitydistribution projected on the resist film 802 by the photomask 810 shownin FIG. 54(a). The simulation conditions are such that the wavelength λof the exposure light 820=193 nm, and the numerical aperture NA of theprojecting optical system of the exposure apparatus=0.6. In this case,0.26×M [μm]≈0.8×M×λ/NA. FIG. 54(b) shows a light intensity distribution,using contour lines of relative light intensity (light intensity whenthe light intensity of exposure light is taken as 1) in atwo-dimensional relative coordination system. As shown in 54(b), thelight intensity distribution transferred onto the resist film 802 isequal to substantially 0 at a position corresponding to the vicinity ofthe center of the mask pattern 812. That is, the light shieldingproperties of the mask pattern 812 is very good.

[0017]FIG. 54(c) shows the simulation results of the light intensitydistribution along line AA′ of FIG. 54(b), and FIG. 54(d) shows theresults of estimating the shape of the resist pattern 803 from thesimulation results of the light intensity distribution shown in FIG.54(b). If the critical intensity is 0.3 as shown in FIG. 54(c), thedistribution shape of the critical intensity value in the lightintensity distribution shown in FIG. 54(b) is substantially matched tothe shape of the mask pattern 812, so that the resist pattern 803(hatched portion) having a substantially desired shape (shape indicatedby a broken line) can be formed, as shown in FIG. 54(d).

[0018]FIG. 55(a) shows another example of the layout of the mask pattern812 on the photomask 810 used in the exposure process shown in FIG.53(c). As shown in FIG. 55(a), the mask pattern 812 has a size (actualsize) of 0.13×M [μm] (M: the magnification factor of an exposureapparatus used in the exposure process).

[0019]FIG. 55(b) shows the simulation results of a light intensitydistribution projected on the resist film 802 by the photomask 810 shownin FIG. 55(a). The simulation conditions are such that the wavelength λof the exposure light 820=193 nm; and the numerical aperture NA of theprojecting optical system of the exposure apparatus=0.6, which are thesame as in the case of FIG. 54(b). In this case, 0.13×M [μm]≈0.4×M×λ/NA.FIG. 55(b) also shows a light intensity distribution using contour linesof relative light intensity in a two-dimensional relative coordinationsystem. As shown in FIG. 55(b), the light intensity distributiontransferred onto the resist film 802 reaches a value of about a half ofthe critical intensity value (0.3) at a position corresponding to thevicinity of the center of the mask pattern 812. That is, the lightshielding properties of the mask pattern 812 are deteriorated because ofan influence of diffraction of the exposure light 820.

[0020]FIG. 55(c) shows the simulation results of the light intensitydistribution along line AA′ of FIG. 55(b), and FIG. 55(d) shows theresults of estimating the shape of the resist pattern 803 from thesimulation results of the light intensity distribution shown in FIG.55(b). If the critical intensity is 0.3 as shown in FIG. 55(c), thedistribution shape of the critical intensity value in the lightintensity distribution shown in FIG. 55(b) is not similar to the shapeof the mask pattern 812, so that the shape of the resist pattern 803(hatched portion) is distorted from a desired shape (shape indicated bya broken line), as shown in FIG. 55(d).

[0021] Summing up, in the conventional method for forming a patternshown in FIGS. 53(a) to 53(d), even if a mask pattern is formed with,for example, a complete light-shielding film, it is difficult to form adesired pattern having a size of a half of λ/NA or less, using the maskpattern. Therefore, there is a limitation regarding the size of a resistpattern that can be formed on a wafer.

[0022] In order to form a desired pattern having a size of a half ofλ/NA or less by emphasizing the contrast of the light intensitydistribution generated by a mask pattern, the following method isproposed by H. Y. Liu et al (Proc. SPIE, Vol. 3334, p. 2 (1998)): Notonly a pattern constituted by a light-shielding film is formed on atransparent substrate as a mask pattern, but also a phase shifter forgenerating a phase difference of 180° with respect to exposure lightbetween the phase shifter and a light-transmitting portion (a portion onwhich the mask pattern is not formed) on the transparent substrate isformed. In this method, when the light-transmitting portion and thephase shifter are arranged while sandwiching the pattern (which may bereferred to as “light-shielding pattern) constituted by thelight-shielding film having a size of a half of λ/NA or less, lightstransmitted through the light-transmitting portion and the phase shifterand diffracted to the back side of the light-shielding pattern canceleach other, so that the light shielding properties of thelight-shielding pattern can be improved.

[0023] Hereinafter, the method of H. Y. Liu et al. will be describedwith reference to the accompanying drawings.

[0024]FIG. 56(a) shows an example of the layout of a desired pattern(resist pattern) to be formed. As shown in FIG. 56(a), a pattern 830 hasa partial pattern 830 a having a size of a half of λ/NA or less.

[0025] FIGS. 56(b) and 56(c) show plan views of conventional twophotomasks used for forming the pattern shown in FIG. 56(a). As shown inFIG. 56(b), a light-shielding film 842 is formed on a transparentsubstrate 841 constituting a first photomask 840, and a first opening843 serving as the light-transmitting portion and a second opening 844serving as the phase shifter are provided in the light-shielding film842 while sandwiching a light-shielding pattern 842 a for forming thepartial pattern 830 a. Furthermore, as shown in FIG. 56(c), alight-shielding pattern 852 for forming the pattern 830 (see FIG. 56(a))in combination with the light-shielding pattern 842 a of the firstphotomask 840 is formed on a transparent substrate 851 constituting asecond photomask 850.

[0026] The method for forming a pattern using the two photomask shown inFIGS. 56(b) and 56(c) is as follows.

[0027] First, a substrate coated with a resist film made of a positiveresist is exposed to light, using the first photomask shown in FIG.56(b). Thereafter, alignment is performed such that a pattern shown inFIG. 56(a) is formed with a latent image formed by the exposure usingthe first photomask and a latent image to be formed by exposure usingthe second photomask shown in FIG. 56(c). Thereafter, exposure isperformed using the second photomask shown in FIG. 56(c), and then theresist film is developed so as to form a resist pattern. Thus, anunwanted pattern (pattern other than the pattern shown in FIG. 56(a))that is formed when development is performed after the exposure usingthe first photomask is removed by the exposure using the secondphotomask. As a result, a pattern having a size of a half of λ/NA orless can be formed.

[0028] In the method of H. Y. Liu et al., the contrast of thelight-shielded image created by a light-shielding pattern is improved byinterposing the light-shielding pattern between the light-transmittingportion and the phase shifter. However, in order to provide this effect,the light-transmitting portion and the phase shifter should be disposedadjacent with a gap of a half of λ/NA or less. In the case where thelight-transmitting portion and the phase shifter are disposedcontinuously on the photomask without interposing the light-shieldingpattern, the light intensity corresponding to the boundary of thelight-transmitting portion and the phase shifter is smaller than thecritical intensity. In other words, a light-shielded image correspondingto the boundary of the light-transmitting portion and the phase shifteris formed. In the case where only a photomask as shown in FIG. 56(b) isused, a light-shielding distribution having an arbitrary shape(distribution of a region having a smaller intensity than the criticalintensity in the light intensity distribution) cannot be formed, so thata pattern having an arbitrary shape cannot be formed. As a results, inorder to form a pattern having a complicated shape such as a patternlayout of a regular LSI, it is essential to perform exposure using thephotomask (second photomask) as shown in FIG. 56(c), in addition toexposure using the photomask (first photomask) as shown in FIG. 56(b).Consequently, the costs of masking is increased, the through-put isreduced because of an increase of the number of processes inlithography, or the production cost is increased.

[0029] The method of H. Y. Liu et al. has another problem as describedbelow.

[0030]FIG. 57(a) shows another example of the layout of a desiredpattern (resist pattern) to be formed. As shown in FIG. 57(a), a pattern860 has a T-shaped partial pattern 860 a having a size of a half of λ/NAor less.

[0031] FIGS. 57(b) and 56(c) show plan views of conventional twophotomasks used for forming the pattern shown in FIG. 57(a). As shown inFIG. 57(b), a light-shielding film 872 is formed on a transparentsubstrate 871 constituting a first photomask 870, and a first opening873 serving as the light-transmitting portion and a second opening 874and a third opening 875 serving as the phase shifters are provided inthe light-shielding film 872 while sandwiching a light-shielding pattern872 a for forming the partial pattern 860 a. Furthermore, as shown inFIG. 57(c), a light-shielding pattern 882 for forming the pattern 860(see FIG. 57(a)) in combination with the light-shielding pattern 872 aof the first photomask 870 is formed on a transparent substrate 881constituting a second photomask 880.

[0032] However, as shown in FIG. 57(b), in the first photomask 870, apart of the light-shielding pattern 872 a is sandwiched between thephase shifters (the second opening 874 and the third opening 875), inother words, the entire light-shielding pattern 872 a cannot be providedonly between the light-transmitting portion and the phase shifter, whichhave opposite phases to each other, so that the light-shieldingproperties of the light-shielding pattern 872 a cannot be improved.Thus, there is a limitation regarding the pattern layout that canutilize the effect of the phase shifter.

DISCLOSURE OF INVENTION

[0033] In view of the above, the present invention has an object offorming a pattern having an arbitrary size or shape by exposure usingone photomask.

[0034] In order to achieve the above object, a first photomask accordingto the present invention is a photomask including a mask pattern havinglight-shielding properties with respect to exposure light provided on atransparent substrate having light-transmitting properties with respectto the exposure light. The mask pattern includes a phase shifter thatgenerates a phase difference of (150+360×n) degrees or more and(210+360×n) degrees or less, where n=an integer, with respect to theexposure light between the phase shifter and a light-transmittingportion in which the mask pattern is not formed on the transparentsubstrate. A first light intensity generated in a light-shielded imageformation region corresponding to the mask pattern on an exposedmaterial by the exposure light transmitted through the phase shifter isnot more than four times a second light intensity generated in thelight-shielded image formation region by the exposure light that istransmitted through the periphery of the mask pattern on the transparentsubstrate and goes into the back side of the mask pattern.

[0035] According to the first photomask, a first light intensitygenerated in a light-shielded image formation region by the exposurelight transmitted through the phase shifter (hereinafter, referred to as“shifter transmitted light”) provided in the mask pattern on thetransparent substrate is not more than four times a second lightintensity generated in the light-shielded image formation region by theexposure light that is transmitted through the periphery of the maskpattern on the transparent substrate and goes into the back side of themask pattern (hereinafter, referred to as “mask pattern diffractedlight”). In this case, the shifter transmitted light and the maskpattern diffracted light have a phase difference of 180 degrees fromeach other, so that the first light intensity and the second lightintensity are cancelled each other. Thus, the light intensity eventuallygenerated in the light-shielded image formation region becomes smallerthan the second light intensity. Therefore, the light-shieldingproperties of the mask pattern can be improved from those of the maskpattern constituted only by a complete light-shielding film, so that apattern having an arbitrary size or shape can be formed by exposureusing one photomask.

[0036] A second photomask according to the present invention is aphotomask including a mask pattern having light-shielding propertieswith respect to exposure light provided on a transparent substratehaving light-transmitting properties with respect to the exposure light.The mask pattern includes a phase shifter that generates a phasedifference of (150+360×n) degrees or more and (210+360×n) degrees orless, where n=an integer, with respect to the exposure light between thephase shifter and a light-transmitting portion in which the mask patternis not formed on the transparent substrate. A first light intensitygenerated in a light-shielded image formation region corresponding tothe mask pattern on an exposed material by the exposure lighttransmitted through the phase shifter is between 0.5 times and 2 times asecond light intensity generated in the light-shielded image formationregion by the exposure light that is transmitted through the peripheryof the mask pattern on the transparent substrate and goes into the backside of the mask pattern.

[0037] According to the second photomask, a first light intensitygenerated in a light-shielded image formation region by the shiftertransmitted light is between 0.5 times and 2 times a second lightintensity generated in the light-shielded image formation region by themask pattern diffracted light. In this case, the shifter transmittedlight and the mask pattern diffracted light have a phase difference of180 degrees from each other, so that the first light intensity and thesecond light intensity are cancelled each other. Thus, the lightintensity eventually generated in the light-shielded image formationregion becomes very small. Therefore, the light-shielding properties ofthe mask pattern can be improved significantly, so that a pattern havingan arbitrary size or shape can be formed by exposure using onephotomask.

[0038] In the first or the second photomask, the phase shifter obtainedby forming a transparent film having a transmittance different from thatof the transparent substrate with respect to the exposure light on thetransparent substrate may be used, or the phase shifter obtained byetching the transparent substrate may be used. Alternatively, the phaseshifter is disposed in an opening provided in the light-shielding filmhaving the same outer shape as that of the mask pattern. In this case,the light-shielding film having the same outer shape as that of the maskpattern may have a transmittance of 15% or less with respect to theexposure light and may generate a phase difference of (−30+360×n)degrees or more and (30+360×n) degrees or less, where n=an integer, withrespect to the exposure light between the light-shielding film and thelight-transmitting portion.

[0039] A first method for forming a pattern according to the presentinvention is a method for forming a pattern using the first photomaskaccording to the present invention and includes forming a positiveresist film on a substrate, irradiating the resist film with theexposure light through the photomask, and forming a resist pattern bydeveloping the resist film irradiated with the exposure light so as toremove portions other than the portion corresponding to the mask patternin the resist film. When the width of the portion corresponding to themask pattern in the resist film is L,

L≦0.4×λ/NA is satisfied,

[0040] where λ is a wavelength of the exposure light, and NA is anumerical aperture of a reduction projection optical system of anexposure apparatus.

[0041] According to the first method for forming a pattern, exposure isperformed using the first photomask according to the present invention,so that the size precision of the resist pattern can be improvedsignificantly, compared with a conventional method. Since defocuscharacteristics in the light intensity distribution eventually generatedin the light-shielded image formation region can be improved, utilizingthe difference in the defocus characteristics between the shiftertransmitted light and the mask pattern diffracted light, and then afocus margin can be improved in the pattern formation.

[0042] A second method for forming a pattern according to the presentinvention is a method for forming a pattern using the first photomaskaccording to the present invention and includes forming a negativeresist film on a substrate, irradiating the resist film with theexposure light through the photomask, and forming a resist pattern bydeveloping the resist film irradiated with the exposure light so as toremove the portion corresponding to the mask pattern in the resist film.When the width of the portion corresponding to the mask pattern in theresist film is L,

L≦0.4×λ/NA is satisfied,

[0043] where λ is a wavelength of the exposure light, and NA is anumerical aperture of a reduction projection optical system of anexposure apparatus.

[0044] According to the second method for forming a pattern, exposure isperformed using the first photomask according to the present invention,so that the size precision of the resist pattern can be improvedsignificantly, compared with a conventional method. Since defocuscharacteristics in the light intensity distribution eventually generatedin the light-shielded image formation region can be improved, utilizingthe difference in the defocus characteristics between the shiftertransmitted light and the mask pattern diffracted light, and thus afocus margin can be improved in the pattern formation.

[0045] A third method for forming a pattern according to the presentinvention is a method for forming a pattern using the photomaskaccording to the second photomask according to the present inventionincludes forming a positive resist film on a substrate, irradiating theresist film with the exposure light through the photomask, and forming aresist pattern by developing the resist film irradiated with theexposure light so as to remove portions other than the portioncorresponding to the mask pattern in the resist film. Wherein when thewidth of the portion corresponding to the mask pattern in the resistfilm is L,

L≦0.4×λ/NA is satisfied,

[0046] where λ is a wavelength of the exposure light, and NA is anumerical aperture of a reduction projection optical system of anexposure apparatus.

[0047] According to the third method for forming a pattern, exposure isperformed using the second photomask according to the present invention,so that the size precision of the resist pattern can be improvedsignificantly, compared with a conventional method. Since defocuscharacteristics in the light intensity distribution eventually generatedin the light-shielded image formation region can be improved, utilizingthe difference in the defocus characteristics between the shiftertransmitted light and the mask pattern diffracted light, and thus afocus margin can be improved in the pattern formation.

[0048] A fourth method for forming a pattern of the present invention isa method for forming a pattern using the second photomask according tothe present invention includes forming a negative resist film on asubstrate, irradiating the resist film with the exposure light throughthe photomask, and forming a resist pattern by developing the resistfilm irradiated with the exposure light so as to remove the portioncorresponding to the mask pattern in the resist film. When the width ofthe portion corresponding to the mask pattern in the resist film is L,

L≦0.4×λ/NA is satisfied,

[0049] where λ is a wavelength of the exposure light, and NA is anumerical aperture of a reduction projection optical system of anexposure apparatus.

[0050] According to the fourth method for forming a pattern, exposure isperformed using the second photomask according to the present invention,so that the size precision of the resist pattern can be improvedsignificantly, compared with a conventional method. Since defocuscharacteristics in the light intensity distribution eventually generatedin the light-shielded image formation region can be improved, utilizingthe difference in the defocus characteristics between the shiftertransmitted light and the mask pattern diffracted light, and thus afocus margin can be improved in the pattern formation.

[0051] It is preferable in the first to the fourth methods for forming apattern that the step of irradiating with the exposure light isperformed using an off-axis illumination method.

[0052] By doing this, also in forming an isolated pattern, optimalexposure can be performed in forming a pattern arranged in a smallcycle, so that a fine pattern having an arbitrary layout can be formedwith high precision.

[0053] When the off-axis illumination method is used, it is preferablethat the direction in which the exposure light is incident to thephotomask is set such that the intensity of the exposure light withwhich the resist film is irradiated has the minimum value in the portioncorresponding to the mask pattern in the resist film. In this case, itis more preferable that the direction in which the exposure light isincident to the photomask is set such that the minimum value is smallerat a defocus position than at a best focus position.

[0054] A first method for producing a photomask according to the presentinvention is a method for forming a photomask including a mask patternhaving light-shielding properties with respect to exposure lightprovided on a transparent substrate having light-transmitting propertieswith respect to the exposure light. The method includes forming a phaseshifter that generates a phase difference of (150+360×n) degrees or moreand (210+360×n) degrees or less, where n=an integer, with respect to theexposure light between the phase shifter and a light-transmittingportion in which the mask pattern is not formed on the transparentsubstrate in a region serving as the mask pattern. The step of forming aphase shifter includes forming a phase shifter such that a first lightintensity generated in a light-shielded image formation regioncorresponding to the mask pattern on an exposed material by the exposurelight transmitted through the phase shifter is proportional to a secondlight intensity generated in the light-shielded image formation regionby the exposure light that is transmitted through a periphery of themask pattern on the transparent substrate and goes into a back side ofthe mask pattern.

[0055] According to the first method for forming a photomask, a phaseshifter is formed in a region serving as a mask pattern such that afirst light intensity generated in a light-shielded image formationregion by the shifter transmitted light is proportional to a secondlight intensity generated in the light-shielded image formation regionby the mask pattern diffracted light. In this case, the shiftertransmitted light and the mask pattern diffracted light have a phasedifference of 180 degrees from each other, so that the first lightintensity and the second light intensity are cancelled each other. Thus,the light intensity eventually generated in the light-shielded imageformation region becomes smaller than the second light intensity.Therefore, the light-shielding properties of the mask pattern can beimproved from those of the mask pattern constituted only by a completelight-shielding film, so that a pattern having an arbitrary size orshape can be formed by exposure using one photomask.

[0056] A second method for producing a photomask according to thepresent invention is a method for forming a photomask including a maskpattern having light-shielding properties with respect to exposure lightprovided on a transparent substrate having light-transmitting propertieswith respect to the exposure light. The method includes forming a phaseshifter that generates a phase difference of (150+360×n) degrees or moreand (210+360×n) degrees or less, where n=an integer, with respect to theexposure light between the phase shifter and a light-transmittingportion in which the mask pattern is not formed on the transparentsubstrate in a region serving as the mask pattern. The step of formingthe phase shifter includes forming the phase shifter such that a firstlight intensity generated in a light-shielded image formation regioncorresponding to the mask pattern on an exposed material by the exposurelight transmitted through the photomask when a periphery of the maskpattern on the transparent substrate is covered with a light-shieldingfilm is proportional to a second light intensity generated in thelight-shielded image formation region by the exposure light transmittedthrough the photomask when the mask pattern is constituted only by alight-shielding film.

[0057] According to the second method for forming a photomask, a phaseshifter is formed in a region serving as a mask pattern such that afirst light intensity generated in a light-shielded image formationregion by the exposure light transmitted through the photomask (that is,the shifter transmitted light) when the periphery of the mask pattern onthe transparent substrate is covered with a light-shielding film isproportional to a second light intensity generated in the light-shieldedimage formation region by the exposure light transmitted through thephotomask (that is, the mask pattern diffracted light) when the maskpattern is constituted only by a light-shielding film. In this case, theshifter transmitted light and the mask pattern diffracted light have aphase difference of 180 degrees from each other, so that the first lightintensity and the second light intensity are cancelled each other. Thus,the light intensity eventually generated in the light-shielded imageformation region becomes smaller than the second light intensity.Therefore, the light-shielding properties of the mask pattern can beimproved from those of the mask pattern constituted only by a completelight-shielding film, so that a pattern having an arbitrary size orshape can be formed by exposure using one photomask. Furthermore, thelight intensities of the shifter transmitted light and the mask patterndiffracted light can be calculated independently from each other, whichmakes calculations of each light intensity easy.

[0058] In the second method for forming a photomask, the light-shieldingfilm constituting the mask pattern may have a transmittance of 15% orless with respect to the exposure light and may generate a phasedifference of (−30+360×n) degrees or more and (30+360×n) degrees orless, where n=an integer, with respect to the exposure light between thelight-shielding film and the light-transmitting portion.

[0059] In the first and the second methods for forming a photomask, itis preferable that the phase shifter has a transmittance different fromthat of the transparent substrate with respect to the exposure light,and the step of forming the phase shifter includes determining aformation position and the transmittance of the phase shifter such thatthe first light intensity is not more than four times the second lightintensity.

[0060] This ensures that the light intensity eventually generated in thelight-shielded image region can be made smaller than the second lightintensity, which ensures that the light-shielding properties of the maskpattern can be improved.

[0061] In the first or the second method for producing a photomask, itis preferable that the phase shifter has a transmittance different fromthat of the transparent substrate with respect to the exposure light,and the step of forming the phase shifter includes determining aformation position and the transmittance of the phase shifter such thatthe first light intensity is between 0.5 times and 2 times the secondlight intensity.

[0062] This ensures that the light intensity eventually generated in thelight-shielded image region can be made very small, so that thelight-shielding properties of the mask pattern can be improvedsignificantly.

[0063] In the first or the second method for producing a photomask, itis preferable that the mask pattern has a light-shielding film havingthe same outer shape, the phase shifter is disposed in an openingprovided in the light-shielding film, and the step of forming the phaseshifter includes determining the width of the opening such that thefirst light intensity is equal to a predetermined value.

[0064] This makes it possible that the transmittance of the phaseshifter can be single, so that the photomask can be produced easily.

[0065] In the first or the second method for producing a photomask, itis preferable that the mask pattern has a light-shielding film havingthe same outer shape, the phase shifter is disposed in an openingprovided in the light-shielding film, and the step of forming the phaseshifter includes determining the width of the opening such that thefirst light intensity is not more than four times the second lightintensity.

[0066] This makes it possible that the transmittance of the phaseshifter can be single, so that the photomask can be produced easily andensures that the light intensity eventually generated in thelight-shielded image region can be made smaller than the second lightintensity, which ensures that the light-shielding properties of the maskpattern can be improved.

[0067] In the first or the second method for producing a photomask, itis preferable the mask pattern has a light-shielding film having thesame outer shape, the phase shifter is disposed in an opening providedin the light-shielding film, and the step of forming the phase shifterincludes determining the width of the opening such that the first lightintensity is between 0.5 times and 2 times the second light intensity.

[0068] This makes it possible that the transmittance of the phaseshifter can be single, so that the photomask can be produced easily andensures that the light intensity eventually generated in thelight-shielded image region can be made very small, which ensures thatthe light-shielding properties of the mask pattern can be improved.

[0069] It is preferable that in the case where the phase shifter isdisposed in an opening provided in a light-shielding film having thesame outer shape as that of the mask pattern, when a width of the maskpattern is Lm,

Lm≦(0.5×λ/NA)×M is satisfied,

[0070] where λ is a wavelength of the exposure light, NA is a numericalaperture of a reduction projection optical system of an exposureapparatus, and M is a magnification factor of the reduction projectionoptical system.

[0071] This makes it possible to set the shape of the opening freely inthe range in which the area of the opening is kept constant, so that thereliability of the photomask can be improved by selecting the shape ofthe opening in view of the degree of attachment between thelight-shielding film and the substrate or the like.

[0072] A third method for producing a photomask is a method for forminga photomask including a mask pattern having light-shielding propertieswith respect to exposure light provided on a transparent substratehaving light-transmitting properties with respect to the exposure lightand includes forming a phase shifter that generates a phase differenceof (150+360×n) degrees or more and (210+360×n) degrees or less, wheren=an integer, with respect to the exposure light between the phaseshifter and a light-transmitting portion in which the mask pattern isnot formed on the transparent substrate and has a transmittance T (where0<T<1) with respect to the exposure light, the phase shifter beingformed in a region serving as the mask pattern. The step of forming thephase shifter includes calculating a light intensity Ia generated in alight-shielded image formation region corresponding to the mask patternon an exposed material by the exposure light transmitted through thephotomask when the mask pattern is constituted only by a light-shieldingfilm, calculating a light intensity Ib generated in the light-shieldedimage formation region by the exposure light transmitted through thephotomask when the transmittance T is 1, and the periphery of the maskpattern on the transparent substrate is covered with a light-shieldingfilm, and determining a formation position and the transmittance T ofthe phase shifter such that 4×Ia≧T×Ib is satisfied.

[0073] According to the third method for forming a photomask, the lightintensity (T×Ib) of the shifter transmitted light and the lightintensity (Ia) of the mask pattern diffracted light can be calculatedindependently from each other, so that each light intensity can becalculated easily. Furthermore, the light intensity of the shiftertransmitted light is not more than four times the intensity of the maskpattern diffracted light, so that the light intensity eventuallygenerated in the light-shielded image formation region becomes smallerthan the second light intensity Therefore, the light-shieldingproperties of the mask pattern can be improved from those of the maskpattern constituted only by a complete light-shielding film, so that apattern having an arbitrary size or shape can be formed by exposureusing one photomask.

[0074] A fourth method for producing a photomask of the presentinvention is a method for forming a photomask including a mask patternhaving light-shielding properties with respect to exposure lightprovided on a transparent substrate having light-transmitting propertieswith respect to the exposure light and includes forming a phase shifterthat generates a phase difference of (150+360×n) degrees or more and(210+360×n) degrees or less, where n=an integer, with respect to theexposure light between the phase shifter and the light-transmittingportion in which the mask pattern is not formed on the transparentsubstrate and has a transmittance T (where 0<T<1) with respect to theexposure light, the phase shifter being formed in a region serving asthe mask pattern. The step of forming the phase shifter includescalculating a light intensity Ia generated in a light-shielded imageformation region corresponding to the mask pattern on an exposedmaterial by the exposure light transmitted through the photomask whenthe mask pattern is constituted only by a light-shielding film,calculating a light intensity Ib generated in the light-shielded imageformation region by the exposure light transmitted through the photomaskwhen the transmittance T is 1, and the periphery of the mask pattern onthe transparent substrate is covered with a light-shielding film, anddetermining a formation position and the transmittance T of the phaseshifter such that 2×Ia≧T×Ib≧0.5×Ia is satisfied.

[0075] According to the fourth method for forming a photomask, the lightintensity (T×Ib) of the shifter transmitted light and the lightintensity (Ia) of the mask pattern diffracted light can be calculatedindependently from each other, so that each light intensity can becalculated easily. Furthermore, the light intensity of the shiftertransmitted light is 0.5 times and 2 times the intensity of the maskpattern diffracted light, so that the light intensity eventuallygenerated in the light-shielded image formation region becomes verysmall. Therefore, the light-shielding properties of the mask pattern canbe improved significantly, so that a pattern having an arbitrary size orshape can be formed by exposure using one photomask.

[0076] In the third or the fourth method for forming a photomask, thelight-shielding film constituting the mask pattern may have atransmittance of 15% or less with respect to the exposure light and maygenerate a phase difference of (−30+360×n) degrees or more and(30+360×n) degrees or less, where n=an integer, with respect to theexposure light between the light-shielding film and thelight-transmitting portion.

[0077] A first method for designing a mask pattern according to thepresent invention is a method for designing a mask pattern for forming aphotomask including a mask pattern having light-shielding propertieswith respect to exposure light provided on a transparent substratehaving light-transmitting properties with respect to the exposure light.The mask pattern has a phase shifter that generates a phase differenceof (150+360×n) degrees or more and (210+360×n) degrees or less, wheren=an integer, with respect to the exposure light between the phaseshifter and a light-transmitting portion in which the mask pattern isnot formed on the transparent substrate. More specifically, the firstmethod for designing a mask pattern includes creating a pattern layoutthat is a layout of the mask pattern and determining a transmittance Tof the phase shifter, generating a plurality of divided patterns bydividing the pattern layout, calculating a light intensity Ic generatedin a light-shielded image formation region corresponding to each of thedivided patterns on an exposed material by the exposure lighttransmitted through the photomask when a light-shielding film isdisposed in the entire pattern layout, calculating a light intensity Iogenerated in the light-shielded image formation region by the exposurelight transmitted through the photomask when an opening is provided in adivided pattern in which the corresponding light intensity Ic is lagerthan a predetermined value of the divided patterns, and alight-shielding film is provided entirely in a portion other than thatportion in the photomask, and providing the phase shifter in a dividedpattern in which Ic/Io>T is satisfied of the divided patterns, providinga light-shielding portion in a divided pattern in which T/4>Ic/Io issatisfied of the divided patterns, and providing a light-shieldingportion having an opening serving as the phase shifter in a dividedpattern in which T≧Ic/Io≧T/4 is satisfied of the divided patterns.

[0078] According to the first method for designing a mask pattern, thelight intensity of the mask pattern diffracted light and the lightintensity of the shifter transmitted light can be calculatedindependently from each other so as to obtain the transmittance of thephase shifter and the size of the opening of the mask enhancer that canmaximize the light-shielding properties based on the ratio of the lightintensities. Thus, the transmittance of the phase shifter and the sizeof the opening of the mask enhancer that can maximize thelight-shielding properties can be obtained easily with respect to anarbitrary layout of the mask pattern.

[0079] A second method for designing a mask pattern according to thepresent invention is a method for designing a mask pattern for forming aphotomask including a mask pattern having light-shielding propertieswith respect to exposure light provided on a transparent substratehaving light-transmitting properties with respect to the exposure light.The mask pattern has a phase shifter that generates a phase differenceof (150+360×n) degrees or more and (210+360×n) degrees or less, wheren=an integer, with respect to the exposure light between the phaseshifter and a light-transmitting portion in which the mask pattern isnot formed on the transparent substrate. More specifically, the secondmethod for designing a mask pattern of the present invention includescreating a pattern layout that is a layout of the mask pattern anddetermining a transmittance T of the phase shifter, generating aplurality of divided patterns by dividing the pattern layout,calculating a light intensity Ic generated in a light-shielded imageformation region corresponding to each of the divided patterns on anexposed material by the exposure light transmitted through the photomaskwhen a light-shielding film is disposed in the entire pattern layout,calculating a light intensity Io generated in the light-shielded imageformation region by the exposure light transmitted through the photomaskwhen an opening is provided in a divided pattern in which thecorresponding light intensity Ic is lager than a predetermined value ofthe divided patterns, and a light-shielding film is provided entirely ina portion other than that portion in the photomask, and providing thephase shifter in a divided pattern in which Ic/Io≧T/4 is satisfied ofthe divided patterns, and providing a light-shielding portion in adivided pattern in which T/4>Ic/Io is satisfied of the divided patterns.

[0080] According to the second method for designing a mask pattern, inaddition to the advantages of the first method for designing a maskpattern, the following advantages can be provided. Since only the phaseshifter and the light-shielding portion are used without using the maskenhancer as the mask pattern, mask pattern data that can realizesufficient light-shielding properties can be created easily.

[0081] A third method for designing a mask pattern according to thepresent invention is a method for designing a mask pattern for forming aphotomask including a mask pattern having light-shielding propertieswith respect to exposure light provided on a transparent substratehaving light-transmitting properties with respect to the exposure light.The mask pattern has a phase shifter that generates a phase differenceof (150+360×n) degrees or more and (210+360×n) degrees or less, wheren=an integer, with respect to the exposure light between the phaseshifter and a light-transmitting portion in which the mask pattern isnot formed on the transparent substrate. More specifically, the thirdmethod for designing a mask pattern of the present invention includescreating a pattern layout that is a layout of the mask pattern anddetermining a transmittance T of the phase shifter, calculating amaximum width Lmax at which a light-shielding effect of the phaseshifter with respect to the exposure light is higher than that of alight-shielding film, and providing a light-shielding portion in apartial pattern whose width is larger than Lmax in the pattern layout,and providing the phase shifter in a partial pattern whose width is Lmaxor less in the pattern layout.

[0082] According to the third method for designing a mask pattern, amask pattern can be designed such that the light-shielding propertiescan be improved based on the width of the pattern layout without usingoptical simulations using mask data, which makes the mask pattern designeasy.

[0083] A fourth method for designing a mask pattern according to thepresent invention is a method for designing a mask pattern for forming aphotomask including a mask pattern having light-shielding propertieswith respect to exposure light provided on a transparent substratehaving light-transmitting properties with respect to the exposure light.The mask pattern has a phase shifter that generates a phase differenceof (150+360×n) degrees or more and (210+360×n) degrees or less, wheren=an integer, with respect to the exposure light between the phaseshifter and a light-transmitting portion in which the mask pattern isnot formed on the transparent substrate. More specifically, the fourthmethod for designing a mask pattern of the present invention includescreating a pattern layout that is a layout of the mask pattern anddetermining two kinds of transmittances T1 and T2 (where T1>T2) of thephase shifter, generating a plurality of divided patterns by dividingthe pattern layout, calculating a light intensity Ic generated in alight-shielded image formation region corresponding to each of thedivided patterns on an exposed material by the exposure lighttransmitted through the photomask when a light-shielding film isdisposed in the entire pattern layout, calculating a light intensity Iogenerated in the light-shielded image formation region by the exposurelight transmitted through the photomask when an opening is provided in adivided pattern in which the corresponding light intensity Ic is lagerthan a predetermined value of the divided patterns, and alight-shielding film is provided entirely in a portion other than thatportion in the photomask, providing the phase shifter in a dividedpattern in which Ic/Io≧T2/4 is satisfied of the divided patterns, andproviding a light-shielding portion in a divided pattern in whichT2/4>Ic/Io is satisfied of the divided patterns, and setting thetransmittance of the phase shifter in a divided pattern in whichIc/Io>(T1 ^(0.5)+T2 ^(0.5))×(T1 ^(0.5)+T2 ^(0.5)) is satisfied of thedivided patterns where the phase shifters are provided to be T1, andsetting the transmittance of the phase shifter in a divided pattern inwhich Ic/Io≦(T1 ^(0.5)+T2 ^(0.5))×(T1 ^(0.5)+T2 ^(0.5)) is satisfied ofthe divided patterns where the phase shifters are provided to be T2.

[0084] According to the fourth method for designing a mask pattern, inaddition to the advantages of the first method for designing a maskpattern, the following advantages can be provided. Since only the phaseshifter and the light-shielding portion are used without using the maskenhancer as the mask pattern, mask pattern data that can realizesufficient light-shielding properties can be created easily.Furthermore, in the situations in which phase shifters having aplurality of transmittances can be used, the phase shifters havingdifferent transmittances can be set such that higher light-shieldingproperties can be realized, and therefore the phase shifters havingdifferent transmittances can be arranged in appropriate positions.

[0085] In the first to the fourth methods for designing a mask pattern,the light-shielding film or the light-shielding portion provided in thepattern layout may have a transmittance of 15% or less with respect tothe exposure light and may generate a phase difference of (−30+360×n)degrees or more and (30+360×n) degrees or less, where n=an integer, withrespect to the exposure light between the light-shielding film or thelight-shielding portion and the light-transmitting portion.

BRIEF DESCRIPTION OF THE DRAWINGS

[0086]FIG. 1(a) is a plan view of a photomask having a mask patternconstituted by a complete light-shielding film, FIG. 1(b) is a viewshowing the manner in which exposure is performed with the photomaskshown in FIG. 1(a), FIG. 1(c) is a diagram showing the light intensitydistribution transferred on an exposed material in the exposure with thephotomask shown in FIG. 1(a), and FIG. 1(d) is a diagram showing thesimulation results of the light intensity distribution transferred on anexposed material when the line width L of a mask pattern is varied inthe exposure with the photomask shown in FIG. 1(a).

[0087]FIG. 2 is a diagram showing a change in the light intensitydistribution transferred on a resist film and a change in the shape of aresist pattern formed after the resist film is developed when the linewidth of a mask pattern is varied in the exposure with the photomask.

[0088]FIG. 3 is a schematic view showing the principle of imageenhancement of the present invention.

[0089]FIG. 4 is a graph showing the simulation results of the lightintensity distribution transferred on an exposed material when the linewidth of a phase shifter is varied in exposure with an image enhancementmask shown in FIG. 3.

[0090]FIG. 5(a) is a diagram showing an example of a design layout of adesired pattern to be formed in a pattern forming method according to afirst embodiment of the present invention, and FIG. 5(b) is a plan viewof a photomask according to the first embodiment of the presentinvention used to form the pattern shown in FIG. 5(a).

[0091] FIGS. 6(a) to (c) are cross-sectional views showing each processof the pattern forming method according to the first embodiment of thepresent invention.

[0092]FIG. 7(a) is a diagram showing the simulation results of the lightintensity distribution projected on a resist film by the photomask shownin FIG. 5(b), FIG. 7(b) is a diagram showing the simulation results ofthe light intensity distribution taken along line AA′ of FIG. 7(a), andFIG. 7(c) is a diagram showing the results of estimating the shape of aresist pattern from the simulation results of the light intensitydistribution shown in FIG. 7(a).

[0093]FIG. 8(a) is a plan view of a photomask having a mask patternconstituted by a phase shifter, and FIG. 8(b) is a view showing themanner in which exposure is performed with a photomask shown in FIG.8(a).

[0094]FIG. 9(a) is a graph showing the simulation results of the lightintensity distribution transferred on an exposed material when thetransmittance of a phase shifter is varied in exposure with a photomaskshown in FIG. 8(a), FIG. 9(b) is a graph showing the simulation resultsof the light intensity generated on an exposed material when thetransmittance of a phase shifter and the line width L of a mask patternare varied in the exposure with a photomask shown in FIG. 8(a), FIG.9(c) is a graph showing the simulation results of the light intensitygenerated on an exposed material when the transmittance of a phaseshifter and the line width L of a mask pattern are varied in theexposure with a photomask shown in FIG. 8(a), represented by contourlines of the light intensity with the transmittance T and the line widthL in the vertical axis and the horizontal axis, respectively.

[0095]FIG. 10 is a schematic view showing the principle of a method ofoverlapping a mask pattern of the present invention regarding the caseof an image enhancement mask having a mask pattern with a line width Lconstituted by a phase shifter with a transmittance T.

[0096] FIGS. 11(a) to (c) are graphs showing the simulation results ofthe light intensity Ih (L, T) generated on an exposed material when thetransmittance T of a phase shifter and the line width L of a maskpattern are varied in the exposure with an image enhancement mask shownin FIG. 10, represented by contour lines of the light intensity with thetransmittance T and the line width L in the vertical axis and thehorizontal axis, respectively.

[0097]FIG. 12 is a schematic view showing the principle of a method ofoverlapping a mask pattern of the present invention regarding the caseof an image enhancement mask having a mask pattern with a square shape(the length of one side is L) constituted by a phase shifter with atransmittance T.

[0098] FIGS. 13(a) to (c) are graphs showing the simulation results ofthe light intensity Ih (L, T) generated on an exposed material when thetransmittance T of a phase shifter and the line width L of a maskpattern are varied in the exposure with an image enhancement mask shownin FIG. 12, represented by contour lines of the light intensity with thetransmittance T and the line width L in the vertical axis and thehorizontal axis, respectively.

[0099] FIGS. 14(a) to (c) are graphs showing the conditions that satisfyIh (L, T)=Ic (L) when the transmittance T of a phase shifter and theline width L of a mask pattern are varied in the exposure with an imageenhancement mask shown in FIG. 10.

[0100]FIG. 15(a) is a diagram showing an example of a design layout of adesired pattern to be formed in a pattern forming method according to asecond embodiment of the present invention, and FIG. 15(b) is a planview of a photomask according to the second embodiment of the presentinvention used to form the pattern shown in FIG. 15(a).

[0101] FIGS. 16(a) to (c) are cross-sectional views showing each processof the pattern forming method according to the second embodiment of thepresent invention.

[0102]FIG. 17(a) is a diagram showing the simulation results of thelight intensity distribution projected on a resist film by the photomaskshown in FIG. 15(b), FIG. 17(b) is a diagram showing the simulationresults of the light intensity distribution taken along line AA′ of FIG.17(a), and FIG. 17(c) is a diagram showing the results of estimating theshape of a resist pattern from the simulation results of the lightintensity distribution shown in FIG. 17(a).

[0103]FIG. 18(a) is a plan view of a photomask having a mask patternconstituted by a light-shielding film and an opening serving as a phaseshifter provided in the light-shielding film, and FIG. 18(b) is a viewshowing the manner in which exposure is performed with the photomaskshown in FIG. 18(a).

[0104]FIG. 19(a) is a graph showing the simulation results of the lightintensity distribution transferred on an exposed material when the widthS of the opening is varied in exposure with a photomask shown in FIG.18(a), and FIG. 19(b) is a graph showing the simulation results of thelight intensity generated on an exposed material when the line width Lof a mask pattern and the width S of the opening are varied in theexposure with a photomask shown in FIG. 18(a), represented by contourlines of the light intensity with the line width L of the mask patternand the width S of the opening in the vertical axis and the horizontalaxis, respectively.

[0105]FIG. 20(a) is a plan view of a photomask having a mask patternconstituted by a light-shielding film and an opening serving as a phaseshifter provided in the light-shielding film, and FIG. 20(b) is a viewshowing the manner in which exposure is performed with the photomaskshown in FIG. 20(a).

[0106]FIG. 21(a) is a graph showing the simulation results of the lightintensity distribution transferred on an exposed material when the widthS of the opening is varied in exposure with a photomask shown in FIG.20(a), FIG. 21(b) is a graph showing the simulation results of the lightintensity generated on an exposed material when the line width L of amask pattern and the width S of the opening are varied in the exposurewith a photomask shown in FIG. 20(a), represented by contour lines ofthe light intensity with the line width L of the mask pattern and thewidth S of the opening in the vertical axis and the horizontal axis,respectively, and FIG. 21(c) is a graph showing the simulation resultsof the light intensity generated on an exposed material when the linewidth L of a mask pattern is varied in the exposure with a photomask inwhich the light-shielding properties of the mask pattern are optimized.

[0107]FIG. 22 is a schematic view showing the principle of a method ofoverlapping a mask pattern of the present invention regarding the caseof an image enhancement mask having a mask pattern with a line width Lconstituted by a mask enhancer of an opening width S.

[0108] FIGS. 23(a) to (c) are graphs showing the simulation results ofthe light intensity Ie (L, S) generated on an exposed material when theline width L of a mask pattern and the opening width S are varied in theexposure with an image enhancement mask shown in FIG. 22, represented bycontour lines of the light intensity with the opening width S and theline width L in the vertical axis and the horizontal axis, respectively.

[0109]FIG. 24 is a schematic view showing the principle of a method ofoverlapping a mask pattern of the present invention regarding the caseof an image enhancement mask having a mask pattern having a square shape(the length of one side is L) constituted by a mask enhancer of anopening width S.

[0110] FIGS. 25(a) to (c) are graphs showing the simulation results ofthe light intensity Ie (L, S) generated on an exposed material when theline width L of a mask pattern and the opening width S are varied in theexposure with an image enhancement mask shown in FIG. 24, represented bycontour lines of the light intensity with the opening width S and themask pattern width L in the vertical axis and the horizontal axis,respectively.

[0111]FIG. 26(a) is a view showing a semi-transparent patternconstituted by a semitransparent film having a line width L and atransmittance T, FIGS. 26(b) to (d) are diagrams showing openingpatterns obtained by providing an opening having a transmittance of 1.0in a transparent substrate, and FIG. 26(e) is a graph showing theresults of evaluating the intensity of light transmitted through theopening with simulations when the opening pattern shown in each of FIGS.26(b) to (d) is irradiated with light while changing the size S from 0to L.

[0112]FIG. 27(a) is a graph showing the results of evaluating theintensity distribution of light transmitted through a semi-transparentfilm with simulations in which the transmittance T is 0.5, when thesemi-transparent pattern shown in FIG. 26(a) is irradiated with light,and FIGS. 27(b) to (d) are graphs showing the results of evaluating theintensity distribution of light transmitted through an opening withsimulations in which the equivalent transmittance T is 0.5, when theopening pattern shown in each of FIGS. 26(b) to (d) is irradiated withlight.

[0113]FIG. 28 is a schematic view showing the principle of an imageenhancement of the present invention when a semi-light-shielding-portionis used as a light-shielding portion constituting a mask pattern in thecase where the line width of a mask pattern constituted by a maskenhancer is smaller than 0.8×λ/NA.

[0114]FIG. 29 is a schematic view showing the principle of an imageenhancement of the present invention when a semi-light-shielding-portionis used as a light-shielding portion constituting a mask pattern in thecase where the line width of a mask pattern constituted by a maskenhancer is larger than 0.8×λ/NA.

[0115] FIGS. 30(a) to (d) are schematic diagrams explaining theadvantages of using a semi-light-shielding portion instead of a completelight-shielding portion as the light-shielding portion constituting amask pattern in an image enhancement mask of the present invention.

[0116] FIGS. 31(a) to (g) are diagrams explaining the dependence of thelight intensity distribution generated on an exposed material byexposure with a mask enhancer on the exposure light incident direction.

[0117] FIGS. 32(a) to (d) are graphs showing the principle of a methodfor improving the defocus characteristics utilizing a mask enhancer.

[0118] FIGS. 33(a) to (d) are graphs showing the principle of a methodfor improving the defocus characteristics utilizing a mask enhancer.

[0119] FIGS. 34(a) to (c) are graphs explaining the dependence of theprofile shape change of the light intensity distribution by defocusingon the exposure light incident direction.

[0120] FIGS. 35(a) to (c) are graphs explaining the dependence of theprofile shape change of the light intensity distribution by defocusingon the exposure light incident direction.

[0121] FIGS. 36(a) to (c) are graphs explaining the dependence of theprofile shape change of the light intensity distribution by defocusingon the exposure light incident direction.

[0122] FIGS. 37(a) to (c) are graphs showing the results of calculatingthe DOF characteristics when exposure is performed using photomaskshaving different sizes of an opening serving as a phase shifter in amask enhancer from each exposure light incident direction.

[0123]FIG. 38(a) is a diagram showing a linear mask pattern parallel tothe Y axis on the coordinate of the light source, FIG. 38(b) is adiagram showing the positions of the light sources that are symmetric tothe X axis and the Y axis on the coordinate of the light source and arefour rotational symmetric, and FIG. 38(c) is a diagram showing theresults of mapping the DOF of a mask pattern constituted by a completelight-shielding film with respect to the position of each light sourcewhen exposure is performed using a circular light source having a radiusof 0.05 from the positions of the light sources with the coordinates (x,y) shown in FIG. 38(b).

[0124]FIG. 39(a) is a diagram showing a mask enhancer having a maskpattern width of L and a width of an opening serving as a phase shifterof S, and FIGS. 39(b) to (d) are diagrams showing the results of mappingthe DOF of a mask pattern constituted by the mask enhancer shown in FIG.39(a) with respect to the position of each light source.

[0125]FIG. 40(a) is a diagram showing the results of plotting DOF valuescorresponding to the position of the light source on the diagonal linein the DOF map shown in each of FIG. 38(c) and FIGS. 39(b) to (d), andFIGS. 40(b) to (d) are diagrams showing the regions in which the DOF isincreased or decreased by 0.05 μm or more from the DOF map shown in FIG.38(c) in the DOF map shown in each of FIGS. 39(b) to (d).

[0126] FIGS. 41(a) to (d) are diagrams showing the results of obtainingthe DOF values corresponding to the position of the light source on thediagonal line based on each DOF map, by obtaining the DOF map of a maskpattern (L/S=0.15/0 μm) constituted by a complete light-shielding filmand the DOF map of a mask pattern (L/S=0.15/0.02, 0.04, 0.06 μm)constituted by a mask enhancer, in each of the cases where a KrF lightsource and a F₂ light source are used with a numerical aperture of areduction projection optical system of an exposure apparatus of 0.6 andwhere an ArF light source is used with a numerical aperture of areduction projection optical system of an exposure apparatus of 0.7 and0.8.

[0127]FIG. 42 is a flowchart showing each process of a mask patterndesign method according to a fourth embodiment of the present invention.

[0128] FIGS. 43(a) to (h) are diagrams explaining the mask patterndesign method according to the fourth embodiment of the presentinvention.

[0129] FIGS. 44(a) and (b) are diagrams explaining the mask patterndesign method according to the fourth embodiment of the presentinvention.

[0130]FIG. 45 is a flowchart showing each process of a mask patterndesign method according to a first variation example of the fourthembodiment of the present invention.

[0131]FIG. 46 is a flowchart showing each process of a mask patterndesign method according to the first variation example of the fourthembodiment of the present invention.

[0132]FIG. 47 is a diagram explaining of the mask pattern design methodaccording to the first variation example of the fourth embodiment of thepresent invention.

[0133]FIG. 48 is a flowchart showing each process of a mask patterndesign method according to a second variation example of the fourthembodiment of the present invention.

[0134] FIGS. 49(a) and (b) are diagrams explaining of the mask patterndesign method according to the second variation example of the fourthembodiment of the present invention.

[0135]FIG. 50 is a flowchart showing each process of a mask patterndesign method according to a third variation example of the fourthembodiment of the present invention.

[0136]FIG. 51 is a flowchart showing each process of a mask patterndesign method according to a fourth variation example of the fourthembodiment of the present invention.

[0137] FIGS. 52(a) and (b) are diagrams explaining of the mask patterndesign method according to the fourth variation example of the fourthembodiment of the present invention.

[0138] FIGS. 53(a) to (d) are cross-sectional views showing each processof a conventional pattern forming method.

[0139]FIG. 54(a) is a diagram showing an example of the layout of a maskpattern on a photomask used in an exposure process shown in FIG. 53(c),FIG. 54(b) is a diagram showing the simulation results of a lightintensity distribution projected on a resist film by the photomask shownin FIG. 54(a), FIG. 54(c) is a diagram showing the simulation results ofthe light intensity distribution along line AA′ of FIG. 54(b), and FIG.54(d) is a diagram showing the results of estimating the shape of theresist pattern from the simulation results of the light intensitydistribution shown in FIG. 54(b).

[0140]FIG. 55(a) is a diagram showing another example of the layout of amask pattern on a photomask used in the exposure process shown in FIG.53(c), FIG. 55(b) is a diagram showing the simulation results of a lightintensity distribution projected on a resist film by the photomask shownin FIG. 55(a), FIG. 55(c) is a diagram showing the simulation results ofthe light intensity distribution along line AA′ of FIG. 55(b), and FIG.55(d) is a diagram showing the results of estimating the shape of theresist pattern from the simulation results of the light intensitydistribution shown in FIG. 55(b).

[0141]FIG. 56(a) is a diagram showing an example of the layout of adesired pattern to be formed in the conventional pattern forming method,and FIGS. 56(b) and (c) are plan views of conventional two photomasksused for forming the pattern shown in FIG. 56(a).

[0142]FIG. 57(a) is a diagram showing another example of the layout of adesired pattern to be formed in the conventional pattern forming method,and FIGS. 57(b) and 56(c) are plan views of conventional two photomasksused for forming the pattern shown in FIG. 57(a).

BEST MODE FOR CARRYING OUT THE INVENTION

[0143] Hereinafter, a method for forming a more effective mask patternhaving higher light-shielding properties than those of a mask patternconstituted by a complete light-shielding film using interference oflight with a 0 degree phase and light with a 180 degree phase, which wasdevised to realize the present invention, will be described withreference of the accompanying drawings.

[0144] First, the reason why there is a lower limit for the pattern sizethat can be formed in the pattern formation with light exposure will bedescribed with reference to FIGS. 1(a) to (d).

[0145]FIG. 1(a) is a plan view of a photomask having a mask patternconstituted by a complete light-shielding film. As shown in FIG. 1(a), amask pattern 11 with a line width L constituted by a completelight-shielding film is formed on a transparent substrate 10.

[0146]FIG. 1(b) shows the manner in which exposure is performed with thephotomask shown in FIG. 1(a), and FIG. 1(c) shows the light intensitydistribution transferred at the position corresponding to line AA′ ofFIG. 1(a) on an exposed material in the exposure with the photomaskshown in FIG. 1(a). As shown in FIG. 1(b), exposure light 12 is shieldedby the mask pattern 11, but a part of the exposure light 12 transmittedthrough in the periphery of the mask pattern 11 in the transparentsubstrate 10, that is, transmitted light 13 diffracts to a region R onthe back of the mask pattern 11. As a result, as shown in FIG. 1(c), thelight intensity Ic is not 0 at the position (0 in the horizontal axis)corresponding to the central portion of the mask pattern 11 on theexposed material.

[0147]FIG. 1(d) shows the simulation results of the light intensitydistribution transferred on the exposed material when the line width Lof the mask pattern 11 is varied in the exposure with the photomaskshown in FIG. 1(a). The optical conditions in the simulations are suchthat the wavelength λ of the exposure light=0.193 μm; the numericalaperture NA of the projecting optical system of the exposureapparatus=0.6; the interference degree (coherence degree) σ of theexposure apparatus=0.8. In this case, the value of 0.4×λ/NA is about0.13 μm. As shown in FIG. 1(d), when the line width L is changed from0.14 μm to 0.1 μm, the light intensity is increased drastically at theposition (0 in the horizontal axis) corresponding to the central portionof the mask pattern 11 on the exposed material. In other words, as theline width L of the mask pattern 11 becomes smaller, light going intothe back side of the mask pattern 11 increases, so that thelight-shielding properties of the mask pattern 11 are deteriorated,which limits the pattern size that can be formed is limited. Morespecifically, when the line width L of the mask pattern 11 is smallerthan about 0.8×λ/NA, the light going into the back side of the maskpattern 11 begins to increase and when the line width L of the maskpattern 11 is smaller than about 0.4×λ/NA, the light going into the backside of the mask pattern 11 increases drastically, so that it becomesdifficult to form a pattern.

[0148]FIG. 2 shows a change in the light intensity distributiontransferred on an exposed material (to be specific, a resist film) and achange in the shape of the resist pattern formed after the resist filmis developed when the line width of a mask pattern is varied in exposurewith a photomask.

[0149] As shown FIG. 2, it is necessary to reduce the line width of amask pattern in order to form a resist pattern having a small linewidth. In the case of a mask pattern having a sufficiently large linewidth as a mask pattern C, the exposure light is sufficiently shielded,so that a resist pattern C having a desired shape can be formed.Furthermore, as the line width of the mask pattern becomes smaller, thelight-shielding properties of the mask pattern are deteriorated, so thatthe light intensity in a region corresponding to the mask pattern in theresist film becomes larger. In this case, when the light going into theback side of the mask pattern from the periphery of the mask pattern(hereinafter, referred to as “mask pattern diffracted light”) does notcause the light intensity to be beyond the critical intensity even ifthe light-shielding properties are deteriorated, the pattern resolutionis possible as in the case of the mask pattern B, and the line width ofthe resist pattern can be reduced by reducing the line width of the maskpattern. However, as in the case of the mask pattern A, when the lightintensity exceeds the critical intensity because of the mask patterndiffracted light, a resist pattern cannot be formed any more.

[0150] Next, a method for realizing a desired light intensitydistribution by canceling the mask pattern diffracted light to let thelight-shielding properties of the mask pattern effectively higher thanthose of the complete light-shielding film (hereinafter, referred to as“image enhancement”) will be described with reference to FIGS. 3 and 4.

[0151]FIG. 3 is a schematic view showing the principle of the imageenhancement of the present invention.

[0152] In general, lights having opposite phases to each other, that is,lights having a phase difference of 180 degrees, have the lightintensity that are opposite in the plus and minus in a phase space.Therefore, when lights having phase difference of 180 degrees interferewith each other, the light intensities of the lights can be cancelled.When the diffracted light from the periphery of the mask patterninterfere with a light having an opposite phase relationship, using thisprinciple, the light intensities of the lights can be cancelled, so thata very high light-shielding effect can be realized by the mask pattern.

[0153] In the image enhancement mask of the present invention shown inFIG. 3, a phase shifter that transmits light having an opposite phase tothat of the light transmitted through a regular light-transmittingportion is provided as a mask pattern, and the intensity of the lighttransmitted through the phase shifter (hereinafter, referred to as“shifter transmitted light) is matched to the intensity of thediffracted light (that is the mask pattern diffracted light) from thelight-transmitting portion in the periphery of the phase shifter, thatis, the periphery of the mask pattern. Thus, the state in which light iscompletely shielded on the back side of the mask pattern can berealized. In this case, the intensity of the shifter transmitted lightcan be adjusted by adjusting the size or the transmittance (with respectto the exposure light) of the phase shifter.

[0154] The intensity of the mask pattern diffracted light in the imageenhancement mask can be obtained by using a light-shielding mask shownin FIG. 3 (a light-shielding film constituted by a completelight-shielding film is provided, instead of the phase shifter of theimage enhancement mask). Furthermore, the intensity of the shiftertransmitted light in the image enhancement mask can be obtained by usinga phase shift transmitted mask shown in FIG. 3 (a light-shieldingportion constituted by a complete light-shielding film is provided,instead of the light-transmitting portion of the image enhancementmask). In this case, when the intensity of the mask pattern diffractedlight is Ic and the intensity of the shifter transmitted light is Io,the condition that can realize the state in which light is completelyshielded on the back side of the mask pattern of the image enhancementmask is Ic=Io.

[0155]FIG. 4 shows the simulation results of the light intensitydistribution transferred on an exposed material when the line width ofthe mask pattern, that is, the phase shifter is varied in the exposurewith the image enhancement mask shown in FIG. 3. In the imageenhancement mask having a phase shifter with each line width, thetransmittance of the phase shifter is optimized such that the maskpattern diffracted light is cancelled by the shifter transmitted lighthaving an opposite phase most satisfactorily. Furthermore, the opticalconditions in the simulations are the same as those of the simulationsshown in FIG. 1(d).

[0156] When the results shown in FIG. 4 are compared with the resultsshown in FIG. 1(d), the exposure method with the image enhancement mask,that is, the image enhancement of the present invention improves thelight-shielding properties of a mask pattern having a line width of lessthan about 0.8×λ/NA, and thus a desired light intensity distribution canbe realized.

[0157] First Embodiment

[0158] Hereinafter, a photomask according to a first embodiment of thepresent invention, a method for producing the same and a method forforming a pattern using the photomask will be described with referenceof the accompanying drawings.

[0159] When the magnification factor of the reduced projecting opticalsystem of the exposure apparatus is M, in general, a mask pattern havinga size M times larger than the designed value of a desired pattern(generally resist pattern) is drawn on a substrate made of a materialhaving a high transmittance with respect to the exposure light(hereinafter, referred to as “transparent substrate”), using a materialsuch as chromium that can be formed into a complete light-shielding filmwith respect to the exposure light, so as to produce a photomask, andexposure is performed using the photomask. As the exposure light, i line(wavelength 365 nm), KrF excimer laser light (wavelength 248 nm), ArFexcimer laser light (wavelength 193 nm), or F₂ excimer laser light(wavelength 157 nm) can be used, for example. In this specification, thesize of the resist pattern may be used to indicate the size of the maskpattern, instead of the actual size on the photomask (a value M timeslarger than the size of the resist pattern).

[0160] A first feature of the first embodiment is as follows. Alight-shielding film portion corresponding to a region in which thelight intensity in the light intensity distribution transferred on anexposed material (to be specific, a resist film) is not sufficientlydecreased by a mask pattern during exposure in the case where the maskpattern corresponding to a desired pattern are produced with alight-shielding film is replaced by a phase shifter, so that a maskpattern is produced, and exposure is performed with a photomask havingthat mask pattern. Herein, the phase shifter refers to alight-transmitting portion that reverses the phase of light transmittedthrough this portion by 180 degrees (to be specific, 150+360×n) degreesor more and (210+360×n) degrees or less (where n is an integer)) withrespect to the phase of the light transmitted through a regularlight-transmitting portion. More specifically, the phase shifter can beproduced, for example, using a transparent film or the like having athickness that generates an optical path difference of a half of thewavelength of the exposure light.

[0161] A second feature of the first embodiment is as follows. The phaseshifter provided as a mask pattern may have a plurality oftransmittances, and a light-shielding film portion that corresponds to aregion having a lower reduction degree in the light intensity in thelight intensity distribution transferred onto an exposed materialthrough a mask pattern constituted only by a light-shielding film isreplaced by a phase shifter having a higher transmittance.

[0162]FIG. 5(a) shows an example of a design layout of a desired pattern(resist pattern) to be formed in the first embodiment. As shown in FIG.5(a), the width of a pattern 20 is 0.13 μm.

[0163]FIG. 5(b) is a plan view of a photomask according to the firstembodiment used to form the pattern shown in FIG. 5(a). As shown in FIG.5(b), the photomask of the first embodiment is obtained by forming amask pattern 40 corresponding to the pattern shown in FIG. 5(a) on atransparent substrate 30. The mask pattern 40 has a size (actual size)of 0.13×M [μm] (M: magnification factor of a reduced projecting opticalsystem of an exposure apparatus). The mask pattern 40 has alight-shielding portion 41 constituted by a light-shielding film such achromium film, a first phase shifter 42 having a transmittance of 10%,and a second phase shifter 43 having a transmittance of 50%.

[0164] For comparison, FIG. 55(a) shows a plan view of a conventionalphotomask used to form the pattern shown in FIG. 5(a) whose mask patternis constituted only by a light-shielding film (see the section of thebackground of the invention), and FIG. 55(b) shows the simulationresults of the light intensity distribution projected onto a resist filmby the photomasks shown in FIG. 55(a). More specifically, in the maskpattern 40 shown in FIG. 5(b), the portion of the light-shielding filmconstituting the mask pattern 812 shown in FIG. 55(a) in which thelight-shielding properties are sufficient is left as it is as thelight-shielding portion 41, and the portion of the light-shielding filmin which the light-shielding properties are not sufficient is replacedby a phase shifter (the first phase shifter 42 and the second phaseshifter 43). Here, the portion corresponding to the edge of the maskpattern 812 in which the light-shielding properties are particularlyweak is replaced by a phase shifter having a higher transmittance (thesecond phase shifter 43).

[0165] FIGS. 6(a) to (c) are cross-sectional views showing each processof the pattern forming method according to the first embodiment of thepresent invention, more specifically, each process of the patternforming method by exposure using the photomask shown in FIG. 5(b).First, as shown in FIG. 6(a), a film to be processed 51 made of a metalfilm, an insulating film or the like is formed on a substrate 50, andthen a positive resist film 52 is formed on the film to be processed 51.Thereafter, as shown in FIG. 6(b), the resist film 52 is irradiated withexposure light 53 through the photomask of the first embodiment obtainedby the mask pattern 40 is formed on the transparent substrate 30 (seeFIG. 5(b)). Thus, the portion corresponding to the mask pattern 40 inthe resist film 52 becomes a non-exposed portion 52 a and other portionsin the resist film 52 become an exposed portion 52 b. Thereafter, asshown in FIG. 6(c), a resist pattern 54 constituted by the non-exposedportion 52 a is formed by developing the resist film 52.

[0166]FIG. 7(a) shows the simulation results of the light intensitydistribution projected on the resist film 52 by the photomask shown inFIG. 5(b). The simulation conditions are that the wavelength λ of theexposure light 53=0.193 nm; the numerical aperture NA of the projectingoptical system of the exposure apparatus=0.6; and the interferencedegree σ of the exposure apparatus=0.8 (hereinafter, these simulationconditions are used when the simulation results are shown, unlessotherwise specified). In this case, the relationship of 0.13×M[μm]≈0.4×M×λ/NA is satisfied with respect to the size of the maskpattern 40 shown in FIG. 5(b). In FIG. 7(a), the light intensitydistribution is shown with contour lines of the relative light intensityin the two-dimensional relative coordinate system.

[0167] When comparing the simulation results shown in FIG. 7(a) and thesimulation results shown in FIG. 55(b), the following can be understood.When the conventional photomask in which the mask pattern is constitutedonly by a light-shielding film is used and the size of the mask patternis narrowed to about a half of λ/NA or less, then the light-shieldingproperties at the edge portion of the mask pattern or the like aredeteriorated significantly. As a result, the shape of the lightintensity distribution is significantly different from a desired patternshape. On the other hand, when the photomask of the first embodiment isused, a phase shifter having a higher transmittance is provided in aportion in which sufficient light-shielding properties cannot beobtained by the light-shielding film in the mask pattern, so thatsufficient light-shielding properties can be realized throughout themask pattern. This, a resist pattern having a shape closer to a desiredshape can be formed. This is achieved by utilizing interference betweenlight with a 0 degree phase and light with a 180 degree phase so as touse the conditions that make the effective light-shielding properties ofthe phase shifter better than those of the light-shielding film.

[0168]FIG. 7(b) shows the simulation results of the light intensitydistribution taken along line AA′ of FIG. 7(a), and FIG. 7(c) shows theresults of estimating the shape of the resist pattern 54 from thesimulation results of the light intensity distribution shown in FIG.7(a). As shown in FIG. 7(b), the critical intensity is 0.3, thedistribution shape of the critical intensity values in the lightintensity distribution shown in FIG. 7(a) is substantially matched tothe shape of the mask pattern 40. As a result, the resist pattern 54(hatched portion) having substantially a desired shape (shape shown bybroken lines), as shown in FIG. 7(c), can be obtained.

[0169] As described above, according to the first embodiment, the phaseshifter is provided in the mask pattern on the photomask, so that themask pattern diffracted light is cancelled by the shifter transmittedlight. Thus, the light-shielding properties of the mask pattern can beimproved from the mask pattern constituted only by a completelight-shielding film, and therefore a pattern having an arbitrary sizeor shape can be formed by exposure using one photomask.

[0170] Hereinafter, the relationship between the transmittance and theline width of the phase shifter provided as a mask pattern in thephotomask of the first embodiment and the light intensity distributionprojected onto an exposed material by the mask pattern will be describedin detail.

[0171]FIG. 8(a) is a plan view of a photomask having a mask patternconstituted by a phase shifter. As shown in FIG. 8(a), a mask pattern 61with a line width L constituted by a transparent film serving as a phaseshifter is formed on a transparent substrate 60.

[0172]FIG. 8(b) shows the manner in which exposure is performed with thephotomask shown in FIG. 8(a). As shown in FIG. 8(b), exposure light 62becomes a first transmitted light 63 after being transmitted through theperiphery of the mask pattern 61 in the transparent substrate 60, andbecomes a second transmitted light 64 after being transmitted throughthe mask pattern 61.

[0173]FIG. 9(a) shows the simulation results of the light intensitydistribution transferred at a position corresponding to line AA′ of FIG.8(a) on an exposed material when the transmittance of the phase shifteris varied in the exposure with the photomask shown in FIG. 8(a). Thesimulation conditions are that the wavelength λ of the exposurelight=0.193 μm; the numerical aperture NA of the projecting opticalsystem of the exposure apparatus=0.6; the interference degree σ of theexposure apparatus=0.8; and the line width L=0.1 μm. The point O on theline AA′ is positioned in the center of the mask pattern 61.

[0174] As shown in FIG. 9(a), as the transmittance of the phase shifterbecomes higher, the light intensity of the position (0 in the horizontalaxis) corresponding to the center O of the mask pattern 61 in theexposed material is decreased and the shape of the light intensitydistribution is better. When the mask pattern 61 is constituted by acomplete light-shielding film (a transmittance of 0%), the shape of thelight intensity distribution is worst. However, in the first embodiment,a higher transmittance of the phase shifter is not always better. Thereason for this will be described below.

[0175]FIG. 9(b) shows the simulation results of the light intensitygenerated at the position corresponding to the point O of FIG. 8(a) onthe exposed material when the transmittance of the phase shifter and theline width L of the mask pattern are varied in the exposure with thephotomask shown in FIG. 8(a).

[0176] As shown in FIG. 9(b), there is a line width L in which theeffective light-shielding properties are highest with respect to themask pattern constituted by a phase shifter of each transmittance, andthere is a line width L in which the light-shielding properties arestarted to be worse than those of the complete light-shielding film. Inthe photomask shown in FIG. 8(a), the light-shielding properties of themask pattern 61 are improved by cancel the light transmitted through theperiphery of the mask pattern 61 on the transparent substrate 60 andgoing into the back side of the mask pattern 61 (that is, mask patterndiffracted light) by the light transmitted through the mask pattern 61(that is, shifter transmitted light). Therefore, when the balancebetween the mask pattern diffracted light and the shifter transmittedlight is optimized, the effective light-shielding properties of the maskpattern 61 are highest. On the other hand, when the shifter transmittedlight is excessive with respect to the mask pattern diffracted light,the effective light-shielding properties of the mask pattern 61 aredecreased and may be lower than the light-shielding properties of themask pattern constituted by a complete light-shielding film in somecases.

[0177]FIG. 9(c) shows the simulation results of the light intensitydistribution generated at the position corresponding to the point O ofFIG. 8(a) on the exposed material when the transmittance T of the phaseshifter and the line width L of the mask pattern are varied in theexposure with the photomask shown in FIG. 8(a), represented by contourlines of the light intensity with the transmittance T and the line widthL in the vertical axis and the horizontal axis, respectively.

[0178] The cross-hatched region shown in FIG. 9(c) shows the combinationcondition of the line width L of the mask pattern and the transmittanceT of the phase shifter that maximize the effective light-shieldingproperties of the mask pattern. In other words, in these combinationconditions, the mask pattern diffracted light and the shiftertransmitted light are cancelled each other. Therefore, the shape of thelight intensity distribution projected on an exposed material throughthe mask pattern can be made close to a desired shape by determining thetransmittance T of the phase shifter that maximizes the effectivelight-shielding properties of each mask pattern with respect to the linewidth L of each mask pattern, based on these combination conditions.

[0179] In FIG. 9(c), the combination conditions (the conditions formaximizing the light-shielding properties) of the line width L and thetransmittance T that maximize the effective light-shielding propertiesof the mask pattern are obtained by actually calculating the lightintensity distribution transferred onto an exposed material usingvarious line widths L of the mask pattern and various transmittances Tof the phase shifter. However, for obtaining the conditions formaximizing the light-shielding properties by this method, calculationtakes a very long time, which makes it difficult, for example, to obtainthe optimal transmittance T of the phase shifter with respect to anarbitrary line width L of the mask pattern.

[0180] Next, a simple method for calculating the conditions formaximizing the light-shielding properties, more specifically, a simplemethod for obtaining the optimal transmittance T of the phase shifterwith respect to an arbitrary line width L of the mask pattern(hereinafter, referred to as a “mask pattern overlapping method”) thathas been found out by the inventors of the present invention will bedescribed.

[0181]FIG. 10 is a schematic view showing the principle of the maskpattern overlapping method of the present invention regarding the caseof a mask pattern with a line width L constituted by a phase shifterwith a transmittance T.

[0182] As shown in FIG. 10, in the exposure using a photomask (imageenhancement mask) having a mask pattern with a line width L constitutedby a phase shifter with a transmittance T, the light intensity generatedat the position corresponding to the center of the mask pattern on theexposed material is taken as Ih (L, T). In the exposure using aphotomask (light-shielding mask) in which a complete light-shieldingfilm is provided as a mask pattern instead of the phase shifter of theimage enhancement mask, the light intensity generated at the positioncorresponding to the center of the mask pattern on the exposed materialis taken as Ic (L). In the exposure using a photomask(light-transmitting mask) in which a regular light-transmitting portionis provided instead of the phase shifter of the image enhancement maskand a light-shielding portion constituted by a complete light-shieldingfilm is provided instead of the light-transmitting portion of the imageenhancement mask, the light intensity generated at the positioncorresponding to the center of the mask pattern on the exposed materialis taken as Io (L). In this case, as described in the principle (seeFIG. 3) of the image enhancement of the present invention, in the imageenhancement mask, the intensity of the mask pattern diffracted lightgenerated at the position corresponding to the center of the maskpattern on the exposed material corresponds to Ic (L), and the lightintensity of the shifter transmitted light generated at the positioncorresponding to the center of the mask pattern on the exposed materialcorresponds to T×Io (L). Therefore, the light intensity Ih (L, T) can beapproximated to a value obtained by converting the light intensity Ic(L) and the light intensity T×Io (L) to the light intensities in a phasespace, overlapping the two light intensities, and squaring the result.That is,

Ih (L, T)=((Ic(L))^(0.5)−(T×Io (L))^(0.5))².

[0183] Therefore, in the image enhancement mask, the condition thatprovides the smallest Ih (L, T), that is, the condition that maximizesthe light-shielding properties of the mask pattern is:

Ic (L)=T×Io (L).

[0184] In other words, the optimal transmittance T of the phase shifterwith respect to an arbitrary line width L of the mask pattern can beobtained with

T=Ic (L)/Io (L).

[0185] FIGS. 11(a) to (c) show the simulation results of the lightintensity Ih (L, T) generated at the position corresponding to thecenter of the mask pattern on the exposed material when thetransmittance T of the phase shifter and the line width L of the maskpattern are varied in the exposure with the image enhancement mask shownin FIG. 10, represented by contour lines of the light intensity with thetransmittance T and the line width L in the vertical axis and thehorizontal axis, respectively. Herein, in each of FIGS. 11(a) to (c),the graph indicating the relationship of T=Ic (L)/Io (L) described aboveis superimposed. The simulation results shown in FIGS. 11(a) to (c) areobtained using different exposure light sources. The simulation resultsshown in FIG. 11(a) are obtained using regular exposure with a circularlight source. The simulation results shown in FIG. 11(b) are obtainedusing annular exposure with an annular light source. The simulationresults shown in FIG. 11(c) are obtained using quadrupole exposure withlight sources positioned at four points on diagonal coordinates. Othersimulation conditions are such that the wavelength of the exposure lightλ=0.193 μm, and the numerical aperture NA of the projecting opticalsystem of the exposure apparatus=0.6.

[0186] As shown in FIGS. 11(a) to (c), the dependence of the lightintensity Ih (L, T) on the transmittance T of the phase shifter and theline width L of the mask pattern is slightly varied depending on theshape of the exposure light source, but the condition that provides thesmallest light intensity Ih (L, T) can be represented accurately by therelationship of T=Ic (L)/Io (L), regardless of the shape of the exposurelight source.

[0187]FIG. 12 is a schematic view showing the principle of the maskpattern overlapping method of the present invention regarding the caseof the image enhancement mask having a mask pattern with a square shape(the length of one side is L) constituted by a phase shifter with atransmittance T. Also in the image enhancement mask shown in FIG. 12,the light intensity of the mask pattern diffracted light generated atthe position corresponding to the center of the mask pattern on theexposed material corresponds to Ic (L), and the light intensity of theshifter transmitted light generated at the position corresponding to thecenter of the mask pattern on the exposed material corresponds to T×Io(L). Therefore, also in the image enhancement mask shown in FIG. 12, theoptimal transmittance T of the phase shifter with respect to anarbitrary line width L of the mask pattern can be obtained with

T=Ic (L)/Io (L).

[0188] FIGS. 13(a) to (c) show the simulation results of the lightintensity Ih (L, T) generated at the position corresponding to thecenter of the mask pattern on the exposed material when thetransmittance T of the phase shifter and the line width L of the maskpattern are varied in the exposure with the image enhancement mask shownin FIG. 12, represented by contour lines of the light intensity with thetransmittance T and the line width L in the vertical axis and thehorizontal axis, respectively. Herein, in each of FIGS. 13(a) to (c),the graph indicating the relationship of T=Ic (L)/Io (L) described aboveis superimposed. The simulation results shown in FIGS. 13(a) to (c) areobtained using different exposure light sources. The simulation resultsshown in FIG. 13(a) are obtained using regular exposure with a circularlight source. The simulation results shown in FIG. 13(b) are obtainedusing annular exposure with an annular light source. The simulationresults shown in FIG. 13(c) are obtained using quadrupole exposure withlight sources positioned at four points on diagonal coordinates. Othersimulation conditions are such that the wavelength of the exposure lightλ=0.193 μm, and the numerical aperture NA of the projecting opticalsystem of the exposure apparatus=0.6.

[0189] As shown in FIGS. 13(a) to (c), the dependence of the lightintensity Ih (L, T) on the transmittance T of the phase shifter and theline width L of the mask pattern is slightly varied depending on theshape of the exposure light source, but the condition that provides thesmallest light intensity Ih (L, T) can be represented accurately by therelationship of T=Ic (L)/Io (L), regardless of the shape of the exposurelight source.

[0190] In other words, there is no limitation regarding the shape of themask pattern to which the mask pattern overlapping method of the presentinvention can be applied.

[0191] More specifically, the transmittance T of the phase shifter thatmaximizes the effective light-shielding properties of a mask patternhaving an arbitrary shape constituted by the phase shifter by the imageenhancement of the present invention can be calculated as follows.

[0192] (1) The light intensity Ic (r) generated at a position rcorresponding to the vicinity of the center of a mask pattern on anexposed material is calculated in exposure using a light-shielding maskprovided with a complete light-shielding film instead of the phaseshifter of the image enhancement mask.

[0193] (2) The light intensity Io (r) generated at a position rcorresponding to the vicinity of the center of a mask pattern on anexposed material is calculated in exposure using a light-transmittingmask in which a regular light-transmitting portion is provided insteadof the phase shifter of the image enhancement mask and a light-shieldingportion constituted by a complete light-shielding film is providedinstead of the light-transmitting portion of the image enhancement mask.

[0194] (3) The optimal transmittance T of the phase shifter is obtainedbased on the relationship T=Ic (L)/Io (L).

[0195] It should be noted that since the upper limit of thetransmittance T is 1, when the transmittance T obtained by T=Ic (L)/Io(L) exceeds 1, the optimal transmittance T is 1.

[0196] In the above description, mask patterns having simple shapes havebeen described, but when a mask pattern has a complex shape, the maskpattern is divided into a plurality of patterns having a simple shape,and the mask pattern overlapping method of the present invention can beapplied to each pattern. By doing this, the optimal transmittance T ofthe phase shifter can be determined for each divided pattern.

[0197] As described above, in the photomask of the first embodiment, theintensity of mask pattern diffracted light is calculated, and thetransmittance T of the phase shifter is calculated such that theintensity of the shifter transmitted light is equal to the intensity ofthe mask pattern diffracted light, and thus the light-shieldingproperties of the mask pattern can be maximized. When a mask pattern hasa complex shape, the mask pattern is divided into a plurality ofpatterns having a simple shape, and the transmittance T of the phaseshifter is calculated such that the intensity of the transmitted lightis equal to the intensity of the diffracted light for each pattern, andthus the light-shielding properties throughout the mask pattern can bemaximized.

[0198] In the first embodiment, in order to maximize the effectivelight-shielding properties of the mask pattern in view of the principleof the image enhancement of the present invention, the transmittance Tof the phase shifter can be determined based on the relationship T=Ic(L)/Io (L). However, if it is sufficient to make the effectivelight-shielding properties of the mask pattern higher than those of themask pattern constituted by a complete light-shielding film, thetransmittance T of the phase shifter may be determined such that therelationship T=Ic (L)/Io (L) is almost satisfied. More specifically,even if the complete light-shielding film is replaced by the phaseshifter, the light-shielding properties of the mask pattern is notimproved any more when the phase shifter having a transmittance of notless than four times the optimal transmittance T obtained from therelationship T=Ic (L)/Io (L) is provided as the mask pattern. The reasonfor this will be described below. As described above, the lightintensity Ih (L, T) generated at the position corresponding to thecenter of the mask pattern on the exposed material through the imageenhancement mask having the mask pattern constituted by the phaseshifter having a line width L and a transmittance T can be estimatedusing the relationship:

Ih (L, T)=((Ic (L))^(0.5)−(T×Io (L))^(0.5))²,

[0199] where Ic (L) is the light intensity of the mask patterndiffracted light and Io(L) is the light intensity of the shiftertransmitted light). Herein, overlapping the Ic (L) and T×Io (L) isoverlapping interference, so that it is necessary to add each lightintensity on the phase space. Therefore, to convert each light intensityto values on the phase space, the square root of each light intensity istaken. The result obtained by adding the square root of each lightintensity in view of each phase of the mask pattern diffracted light andthe shifter transmitted light corresponds to overlapping of the lightintensities on the phase space, and further in order to convert theresult to regular light intensity, the result is squared.

[0200] As described above, when the square of Ih (L, T), that is,((Ic(L))^(0.5)−(T×Io (L))^(0.5))² is minimized, in other words, when thelight-shielding effect by the mask pattern is highest, Ic (L)=T×Io (L)is satisfied, and therefore the optimized transmittance T (hereinafter,referred to as the optimal transmittance Tb) of the phase shifter can beobtained based on:

Tb=Ic(L)/Io (L).

[0201] On the other hand, the condition in which the shifter transmittedlight becomes excessive, and the effective light-shielding properties ofthe mask pattern are deteriorated to be equal to those of the maskpattern constituted by a complete light-shielding film can be Ih (L,T)=Ic (L), that is,

−((Ic (L))^(0.5)−(T×Io (L))^(0.5))=(Ic(L))^(0.5).

[0202] In this case, since

(T×Io (L))^(0.5))²=2×(Ic (L))^(0.5)

[0203] is satisfied, and therefore

T×Io (L)=4×(Ic (L))

[0204] is satisfied. In other words, when the light intensity of theshifter transmitted light reaches four times the light intensity of themask pattern diffracted light, the effective light-shielding propertiesof the mask pattern becomes equal to those of the mask patternconstituted by a complete light-shielding film. The transmittance T ofthe phase shifter that satisfies this condition (hereinafter, referredto as “limit transmittance Tw) can be obtained based on:

Tw=4×Ic (L)/Io (L)=4×Tb.

[0205] Therefore, when the phase shifter having a transmittance of notless than four times the optimal transmittance Tb is provided as themask pattern instead of the complete light-shielding film, the effectivelight-shielding properties of the mask pattern are lower than those ofthe mask pattern constituted by the complete light-shielding film. Inother words, when the transmittance of the phase shifter is not morethan four times the optimal transmittance Tb, the effectivelight-shielding properties of the mask pattern can be improved byproviding the phase shifter as the mask pattern instead of the completelight-shielding film.

[0206] FIGS. 14(a) to (c) show the conditions that satisfy Ih (L, T)=Ic(L) when the transmittance T of the phase shifter and the line width Lof the mask pattern are varied in the exposure with the imageenhancement mask shown in FIG. 10. Herein, in each of FIGS. 14(a) to(c), the graph (Tw is represented by T in the FIGS. 14(a) to (c))indicating the relationship of Tw=4×Ic (L)/Io (L) described above issuperimposed. The simulation results shown in FIGS. 14(a) to (c) areobtained using different exposure light sources. The simulation resultsshown in FIG. 14(a) are obtained using regular exposure with a circularlight source. The simulation results shown in FIG. 14(b) are obtainedusing annular exposure with an annular light source. The simulationresults shown in FIG. 14(c) are obtained using quadrupole exposure withlight sources positioned at four points on diagonal coordinates. Othersimulation conditions are such that the wavelength of the exposure lightλ=0.193 μm, and the numerical aperture NA of the projecting opticalsystem of the exposure apparatus=0.6.

[0207] As shown in FIGS. 14(a) to (c), the dependence of the conditionthat satisfies Ih (L, T)=Ic (L) on the transmittance T of the phaseshifter and the line width L of the mask pattern is slightly varieddepending on the shape of the exposure light source, but the conditionthat satisfies Ih (L, T)=Ic (L) can be represented accurately by therelationship of T=4×Ic (L)/Io (L), regardless of the shape of theexposure light source.

[0208] In the above description, the limit transmittance Tw of the phaseshifter with respect to an arbitrary line width L of the mask patternhas been obtained, but on the other hand, the limit line width Lo of themask pattern with respect to a predetermined transmittance To of thephase shifter can be obtained. More specifically, Ic (L)/Io (L) isdecreased with an increase of the line width L of the mask pattern.Therefore, when the line width L providing that Ic (L)/Io (L) is To/4with respect to a predetermined transmittance To of the phase shifter istaken as the limit line width Lo, the effective light-shieldingproperties of the mask pattern are deteriorated to a larger extent whenthe phase shifter is used instead of a light-shielding film in the maskpattern having a line width of a limit line width Lo or more. Therefore,when the phase shifter having a predetermined transmittance To isprovided in a mask pattern having an arbitrary layout, it is preferableto provide the phase shifter in a mask pattern portion having a linewidth of not more than the limit line width Lo determined by therelationship of Ic (L)/Io (L)=To/4, and to provide a light-shieldingfilm in a mask pattern portion having a line width of the limit linewidth Lo or more. By doing this, the effective light-shieldingproperties of the entire mask pattern can be improved, compared with thecase where the entire mask pattern is formed by a light-shielding film.The size at which the arrangement of the phase shifter and thearrangement of the light-shielding film are switched is not necessarilythe limit line width Lo determined by the relationship of Ic (L)/Io(L)=To/4, and can be any line width of not more than the limit linewidth Lo.

[0209] In the above description, the optimal transmittance T is obtainedbased on Tb=Ic (L)/Io (L) and the limit transmittance Tw is obtainedbased on Tw=4×Ic (L)/Io (L)=4×Tb, but for more generalized situations,the transmittance T of the phase shifter can be determined in thefollowing manner. To reduce the light intensity Ih generated at theposition corresponding to the center of the mask pattern on an exposedmaterial to 1/D of the intensity Ic of the mask pattern diffractedlight, the transmittance T that satisfies the following inequality canbe used.

−((Ic)^(0.5)−(T×Io)^(0.5))<(Ic/D)^(0.5)<((Ic)^(0.5)−(T×Io)^(0.5))

[0210] From this relationship, the following range can be obtained asthe acceptable range of the transmittance T:

(Ic/Io)×((D−D ^(0.5))/D)×((D−D ^(0.5))/D)<T<(Ic/Io)×((D+D^(0.5))/D)×((D+D ^(0.5))/D)

[0211] More specifically, in the case of D=3, the acceptable range ofthe transmittance T is between 0.18 times and 2.5 times the value of(Ic/Io). In the case of D=5, the acceptable range of the transmittance Tis between 0.31 times and 2.1 times the value of (Ic/Io). In the case ofD=10, the acceptable range of the transmittance T is between 0.48 timesand 1.7 times the value of (Ic/Io). It is not necessary to maximize thelight-shielding properties of all the mask patterns in practice, so thatif the transmittance T of the phase shifter is between about ⅓ and 2times the value of (Ic/Io), the light-shielding properties of the maskpattern can be improved sufficiently.

[0212] Furthermore, when two phase shifters having, for example,different transmittances can be used as mask patterns, which of the twophase shifters is the phase shifter whose transmittance can realizehigher light-shielding properties can be determined by the followingmethod. When the transmittances of the two phase shifters are T1 and T2(T1>T2), respectively, the condition that provides the higherlight-shielding properties using the phase shifter having atransmittance T1 than using the phase shifter having a transmittance T2is:

(Ic ^(0.5)−(T 1×Io)^(0.5))×(Ic ^(0.5)−(T 1×Io)^(0.5))<(Ic ^(0.5)−(T2×Io)^(0.5))×(Ic ^(0.5)−(T 2×Io)^(0.5))

[0213] When this inequality is rearranged,

Ic/Io>(T 1 ^(0.5) +T 2 ^(0.5))×(T 1 ^(0.5) +T 2 ^(0.5))/2

[0214] can be obtained. Therefore, in the mask pattern portion in which

Ic/Io>(T 1 ^(0.5) +T 2 ^(0.5))×(T 1 ^(0.5) +T 2 ^(0.5))/2

[0215] is satisfied, the phase shifter having a transmittance T1 can beselected, and in the mask pattern portion in which

Ic/Io≦(T 1 ^(0.5) +T 2 ^(0.5))×(T 1 ^(0.5) +T 2 ^(0.5))/2

[0216] is satisfied, the phase shifter having a transmittance T2 can beselected.

[0217] Furthermore, in a method for forming a pattern of the firstembodiment, that is, a method for forming a pattern using the photomaskof the first embodiment, a positive resist or a negative resist film canbe used as the resist film. When a positive resist film is used, aresist pattern having a mask pattern shape can be formed by developingthe positive resist film irradiated with exposure light, and removingportions other than the portion corresponding to the mask pattern in thepositive resist film. When a negative resist film is used, a resistpattern having an opening with a mask pattern shape can be formed bydeveloping the negative resist film irradiated with exposure light, andremoving the portion corresponding to the mask pattern in the negativeresist film. Regardless of whether the positive resist film is used orthe negative resist film is used, when the width L of the mask patternis smaller than about 0.4×λ/NA, the precision of the size of the resistpattern can be improved significantly, compared with the conventionalmethods.

[0218] Second Embodiment

[0219] Hereinafter, a photomask according to a second embodiment of thepresent invention, a method for producing the same and a method forforming a pattern using the photomask will be described with referenceof the accompanying drawings.

[0220] The feature of the second embodiment is as follows. As in thefirst embodiment, in the case where a light-shielding film portioncorresponding to a region in which the light intensity in the lightintensity distribution transferred on an exposed material (to bespecific, a resist film) is not sufficiently decreased by a mask patternduring exposure when the mask pattern corresponding to a desired patternis produced with a light-shielding film is replaced by a phase shifterso as to produce a mask pattern, and exposure is performed with aphotomask having that mask pattern.

[0221] The second embodiment is different from the first embodiment inthe following aspects. In the first embodiment, a plurality oftransmittances of a phase shifter provided as a mask pattern are presentin order to control the intensity of the shifter transmitted light bythe transmittance of the phase shifter. On the other hand, in the secondembodiment, all the phase shifters provided as a mask pattern have thesame transmittance, and the intensity of the shifter transmitted lightis controlled by covering partially the phase shifter with alight-shielding film.

[0222]FIG. 15(a) shows an example of a design layout of a desiredpattern (resist pattern) to be formed in the second embodiment. As shownin FIG. 15(a), the width of a pattern 70 is 0.13 μm. The design layoutof the pattern 70 is the same as the design layout of the pattern 20 tobe formed in the first embodiment shown in FIG. 5(a).

[0223]FIG. 15(b) is a plan view of a photomask according to the secondembodiment used to form the pattern shown in FIG. 15(a). As shown inFIG. 15(b), the photomask of the second embodiment is obtained byforming a mask pattern 90 corresponding to the pattern shown in FIG.15(a) on a transparent substrate 80. The mask pattern 90 has a size(actual size) of 0.13×M [μm] (M: magnification factor of a reducedprojecting optical system of an exposure apparatus). The mask pattern 90has a light-shielding portion 91 constituted by a light-shielding filmsuch a chromium film, and a phase shifter 92 disposed in the openingprovided in the light-shielding film.

[0224] When comparing the photomask of the second embodiment shown inFIG. 15(b) with the photomask of the first embodiment shown in FIG.5(b), the following can be understood. In the second embodiment, withrespect to a region in which a phase shifter (the second phase shifter43) having a high transmittance is provided in the first embodiment, alarge opening is provided in a light-shielding film serving as thelight-shielding portion 91, and the opening is used as the phase shifter92. With respect to a region in which a phase shifter (the first phaseshifter 42) having a low transmittance is provided in the firstembodiment, a small opening is provided in a light-shielding filmserving as the light-shielding portion 91, and the opening is used asthe phase shifter 92.

[0225] FIGS. 16(a) to (c) are cross-sectional views showing each processof the pattern forming method according to the second embodiment, morespecifically, are cross-sectional view showing each process of a methodfor forming a pattern by exposure using the photomask shown in FIG.15(b). First, as shown in FIG. 16(a), a film to be processed 101 made ofa metal film, an insulating film or the like is formed on a substrate100, and then a positive resist film 102 is formed on the film to beprocessed 101. Thereafter, as shown in FIG. 16(b), the resist film 102is irradiated with the exposure light 103 through the photomask (seeFIG. 15(b)) of the second embodiment obtained by forming a mask pattern90 on a transparent substrate 80. Thus, a portion corresponding to themask pattern 90 in the resist film 102 becomes a non-exposed portion 102a, and other portions in the resist film 102 become an exposed portion102 b. Thereafter, as shown in FIG. 16(c), a resist pattern 104constituted by the non-exposed portion 102 a is formed by developing theresist film 102.

[0226]FIG. 17(a) shows the simulation results of the light intensitydistribution projected on the resist film 102 by the photomask shown inFIG. 15(b). The simulation conditions are that the wavelength λ of theexposure light 103=0.193 nm; the numerical aperture NA of the projectingoptical system of the exposure apparatus=0.6; and the interferencedegree σ of the exposure apparatus=0.8. In this case, the relationshipof 0.13×M [μm]≈0.4×M×λ/NA is satisfied with respect to the size of themask pattern 90 shown in FIG. 15(b). In FIG. 17(a), the light intensitydistribution is shown with contour lines of the relative light intensityin the two-dimensional relative coordinate system.

[0227] When comparing of the simulation results of the second embodimentshown in FIG. 17(a) and the simulation results of the first embodimentshown in FIG. 7(a), the following can be understood. When the photomaskof the second embodiment is used, a larger opening is provided in aportion in which sufficient light-shielding properties cannot beobtained by the light-shielding film in the mask pattern, so thatsufficient light-shielding properties can be realized throughout themask pattern. Therefore, as in the first embodiment, a resist patternhaving a shape closer to a desired shape can be formed.

[0228]FIG. 17(b) shows the simulation results of the light intensitydistribution taken along line AA′ of FIG. 17(a), and FIG. 17(c) showsthe results of estimating the shape of the resist pattern 104 from thesimulation results of the light intensity distribution shown in FIG.17(a). As shown in FIG. 17(b), the critical intensity is 0.3, thedistribution shape of the critical intensity values in the lightintensity distribution shown in FIG. 17(a) is substantially matched tothe shape of the mask pattern 90. As a result, the resist pattern 104(hatched portion) having substantially a desired shape (shape shown bybroken lines), as shown in FIG. 17(c), can be obtained.

[0229] As described above, according to the second embodiment, the phaseshifter is provided in the mask pattern on the photomask, so that themask pattern diffracted light is cancelled by the shifter transmittedlight. Thus, the light-shielding properties of the mask pattern can beimproved from the mask pattern constituted only by a completelight-shielding film, and therefore a pattern having an arbitrary sizeor shape can be formed by exposure using one photomask.

[0230] Hereinafter, the advantages of the second embodiment over thefirst embodiment will be described. As described above, theoretically,in the case where a mask pattern corresponding to a desired pattern isformed using a light-shielding film, the effective light-shieldingproperties can be improved throughout the mask pattern by replacing aportion in which the effective light-shielding properties aredeteriorated in the light-shielding film by a phase shifter having anoptimal transmittance. In this case, it is necessary to form the phaseshifter as a deposited film on a transparent substrate made of quartz orthe like, which is a material transmitting exposure light, and it isalso necessary to provide deposited films made of materials havingdifferent transmittances in different positions on the transparentsubstrate. However, this is difficult in terms of time and costs on maskproduction. On the other hand, when it is attempted to control thetransmittance of the phase shifter by the thickness of the depositedfilm instead of the material of the deposited film, the thickness of thedeposited film is limited to the thickness that generates an opticalpath difference corresponding to a phase difference of 180 degrees.Therefore, it is difficult to change the transmittance of the phaseshifter in each portion of the mask pattern by changing the thickness ofthe deposited film made of a single material. On the other hand, in thesecond embodiment, the shifter transmitted light is controlled, not bythe transmittance of the phase shifter, but by the size of the openingprovided in the mask pattern (more specifically, the opening provided inthe light-shielding film having the outline shape of the mask pattern),so that the transmittance of the phase shifter disposed in the openingcan be uniform. In this case, it is of course possible that there are aplurality of transmittances.

[0231] Hereinafter, the relationship between the width of the openingprovided in the mask pattern of the photomask of the second embodimentand the light intensity distribution projected onto an exposed materialthrough the mask pattern will be described in detail. In the secondembodiment, the aspect of using the principle of the image enhancementof canceling the mask pattern diffracted light by the shiftertransmitted light is common with the first embodiment. In the firstembodiment, the transmittance of the phase shifter is set appropriatelywith respect to the line width of the mask pattern, whereas in thesecond embodiment, the width of the opening is set appropriately withrespect to the line width of the mask pattern.

[0232]FIG. 18(a) is a plan view of a photomask having a mask patternconstituted by a light-shielding film and an opening provided with thelight-shielding film and serving as a phase shifter. As shown in FIG.18(a), a transparent film 111 patterned into a mask pattern shape andserving as a phase shifter is formed on a transparent substrate 110, anda light-shielding film 112 such as a chromium film is formed so as tocover the transparent film 111. Furthermore, and an opening 113 isprovided in the light-shielding film 112 so as to expose the transparentfilm 111, and thus the opening 113 functions as a phase shifter. In FIG.18(a), the transmittance (T) of the transparent film 111 is 50%, themask pattern line width is L, and the width of the opening 113(hereinafter, referred to as “opening width”) is S.

[0233]FIG. 18(b) shows the manner in which exposure is performed withthe photomask shown in FIG. 18(a). As shown in FIG. 18(b), exposurelight 114 becomes a first transmitted light 115 after being transmittedthrough the periphery of the mask pattern on the transparent substrate110, and becomes a second transmitted light 116 after being transmittedthrough the opening 113.

[0234]FIG. 19(a) shows the simulation results of the light intensitydistribution transferred at a position corresponding to line AA′ of FIG.18(a) on an exposed material when the opening width S is varied in theexposure with the photomask shown in FIG. 18(a). The simulationconditions are that the wavelength λ of the exposure light=0.193 μm; thenumerical aperture NA of the projecting optical system of the exposureapparatus=0.6; the interference degree a of the exposure apparatus=0.8;and the line width L=0.1 μm. The point O on the line AA′ is positionedin the center of the mask pattern.

[0235] As shown in FIG. 19(a), as the opening width S becomes higher,the light intensity of the position (0 in the horizontal axis)corresponding to the center O of the mask pattern in the exposedmaterial is decreased and the shape of the light intensity distributionis better. When the opening width S is 0 (the mask pattern isconstituted by a complete light-shielding film), the shape of the lightintensity distribution is worst. In other words, a comparison with thesimulation results shown in FIG. 9(a) indicates that increasing thewidth of the opening provided in the mask pattern brings about the sameeffect as increasing the transmittance of the phase shifter provided inthe mask pattern.

[0236]FIG. 19(b) shows the simulation results of the light intensitygenerated at the position corresponding to the point O of FIG. 18(a) onthe exposed material when the mask pattern line width L and the openingwidth S are varied in the exposure with the photomask shown in FIG.18(a), represented by contour lines of the light intensity with the maskpattern line width L and the opening width S in the vertical axis andthe horizontal axis, respectively.

[0237] The cross-hatched region shown in FIG. 19(b) shows thecombination condition of the mask pattern line width L and the openingwidth S that maximize the effective light-shielding properties of themask pattern. In other words, in these combination conditions, the lightintensities of the mask pattern diffracted light and the shiftertransmitted light are cancelled each other. Therefore, the shape of thelight intensity distribution projected on an exposed material throughthe mask pattern can be made close to a desired shape by determining theopening width S that maximizes the effective light-shielding propertiesof each mask pattern with respect to the mask pattern line width L,based on these combination conditions.

[0238] In the photomask shown in FIG. 18(a), even if the opening width Sis equal to the mask pattern line width L (the light-shielding film 112is not provided on the transparent film 111 serving as a phase shifter),the largest value of the shifter transmitted light is limited by thetransmittance of the transparent film 111. On the other hand, in thesecond embodiment, it is preferable that the transmittance of the phaseshifter is high, unless there is no specific reason to suppress thelargest value of the transmittance of the phase shifter.

[0239] Therefore, in the second embodiment, it is preferable to use aphotomask in as shown in FIG. 20(a), that is, a photomask provided witha phase shifter formed by etching the transparent substrate by athickness that can generate an optical path difference corresponding toa phase difference of 180 degrees, instead of the photomask shown inFIG. 18(a). In this case, the transmittance of the phase shifter issubstantially equal to the transmittance of the transparent substrate.In this specification, the transmittance of the transparent substrate isused as the reference (1.0) of the transmittance.

[0240]FIG. 20(a) is a plan view of a photomask having a mask patternconstituted by a light-shielding film and an opening serving as a phaseshifter provided in the light-shielding film. As shown in FIG. 20(a), alight-shielding film 121 such as a chromium film having the outer shapeof the mask pattern is formed on a transparent substrate 120. An opening123 is formed in the light-shielding film 121 and an etched portion 122serving as a phase shifter is formed below the opening 123 in thetransparent substrate 120. In the FIG. 20(a), the mask pattern linewidth is L, and the width of the opening 123 (hereinafter, referred toas “opening width”) is S.

[0241]FIG. 20(b) shows the manner in which exposure is performed withthe photomask shown in FIG. 20(a). As shown in FIG. 20(b), exposurelight 124 becomes a first transmitted light 125 after being transmittedthrough the periphery of the mask pattern on the transparent substrate120, and becomes a second transmitted light 126 after being transmittedthrough the opening 123.

[0242]FIG. 21(a) shows the simulation results of the light intensitydistribution transferred at a position corresponding to line AA′ of FIG.20(a) on an exposed material when the opening width S is varied in theexposure with the photomask shown in FIG. 20(a). The simulationconditions are the same as those in the case of FIG. 19(a). The point Oon the line AA′ is positioned in the center of the mask pattern.

[0243] As shown in FIG. 21(a), as the opening width S becomes larger,the light intensity of the position (0 in the horizontal axis)corresponding to the center O of the mask pattern in the exposedmaterial is decreased and the shape of the light intensity distributionis better.

[0244] When the opening width S is 0 (the mask pattern is constituted bya complete light-shielding film), the shape of the light intensitydistribution is worst. Furthermore, a comparison with the simulationresults shown in FIG. 19(a) indicates that the light-shieldingproperties of the mask pattern are improved further because thetransmittance of the phase shifter is increased.

[0245]FIG. 21(b) shows the simulation results of the light intensitygenerated at the position corresponding to the point O of FIG. 21(a) onthe exposed material when the mask pattern line width L and the openingwidth S are varied in the exposure with the photomask shown in FIG.20(a), represented by contour lines of the light intensity with the maskpattern line width L and the opening width S in the vertical axis andthe horizontal axis, respectively. A comparison of the simulationresults shown in FIG. 21(b) with the simulation results shown in FIG.19(a) indicates that in FIG. 21(b), the effective light-shieldingproperties of the mask pattern are kept high also with respect to asmaller mask pattern line width L because the transmittance of the phaseshifter is increased.

[0246] The cross-hatched region shown in FIG. 21(b) shows thecombination condition of the mask pattern line width L and the openingwidth S that maximize the effective light-shielding properties of themask pattern. In other words, in these combination conditions(hereinafter, referred to as “light-shielding property maximizingconditions), the light intensities of the mask pattern diffracted lightand the shifter transmitted light are cancelled each other.

[0247] As the photomask shown in FIG. 21(b), in the light-shieldingproperty maximizing conditions, the relationship that the opening widthS is larger as the mask pattern line width L is smaller is satisfied. Inother words, in the second embodiment, when the mask pattern line widthL is sufficiently large, the opening width S is made 0, and the openingwidth S is increased according to the light-shielding propertymaximizing conditions shown in FIG. 21(b) as the mask pattern line widthL is decreased, and when mask pattern line width L is decreased to someextent, the mask pattern is constituted only by the phase shifter, inother words, the structure of the mask pattern is changed continuouslywith the mask pattern line width L. Thus, the light-shielding propertiesof the mask pattern can be constantly optimized.

[0248]FIG. 21(c) shows the simulation results of the light intensitygenerated at the position corresponding to the center of the maskpattern on an exposed material when the line width L of the mask patternis varied in the exposure with the photomask (“the optimized mask” inthe drawing) in which the light-shielding properties of the mask patternare optimized as described above. FIG. 21(c) also shows, for comparison,the simulation results of the light intensity generated at the positioncorresponding to the center of the mask pattern on an exposed materialwhen the line width L of the mask pattern is varied in the exposure withthe conventional photomask (“the chromium mask” in the drawing) in whicha mask pattern constituted only by a complete light-shielding film suchas a chromium film is provided).

[0249] As shown FIG. 21(c), in the exposure using the chromium mask,when the mask pattern line width L is about 0.2 μm or less, thelight-shielding properties of the mask pattern are started todeteriorate. On the other hand, in the exposure using the optimizedmask, the light-shielding properties of the mask pattern can beprevented from deteriorating until the mask pattern line width L isabout 0.1 μm or less.

[0250] In FIG. 19(b) or 21(b), the combination conditions of the maskpattern line width L and the opening width S that maximize the effectivelight-shielding properties of the mask pattern (the light-shieldingproperty maximizing conditions) are obtained by actually calculating thelight intensity distribution transferred on an exposed material usingvarious mask pattern line widths L and opening widths S. However, forobtaining the light-shielding property maximizing conditions by thismethod, calculation takes a very long time, which makes it difficult,for example, to obtain the optimal opening width S with respect to anarbitrary mask pattern line width L of the mask pattern.

[0251] Next, a simple method for calculating the light-shieldingproperty maximizing conditions, more specifically, a simple method forobtaining the optimal opening width S with respect to an arbitrary maskpattern line width L (hereinafter, referred to as a “mask patternoverlapping method”) that is found out by the inventor of the presentinvention will be described. In the following description, calculationresults are shown, assuming that the transmittance of the phase shifteris the same as the transmittance (1.0) of the transparent substrateserving as a mask substrate. However, when the transmittance of thephase shifter is not the same as that of the transparent substrate, theintensity of shifter transmitted light transmitted through the openingis calculated based on the difference in the transmittance.

[0252]FIG. 22 is a schematic view showing the principle of the maskpattern overlapping method of the present invention regarding the caseof a mask pattern with a line width L constituted by a mask enhancerwith an opening width S. In the following description, the structure ofthe present invention in which an opening serving as a phase shifter isprovided in a light-shielding film in a mask pattern is referred to as a“mask enhancer”.

[0253] As shown in FIG. 22, in the exposure using a photomask (imageenhancement mask) having a mask pattern with a line width L constitutedby a mask enhancer with an opening width S, the light intensitygenerated at the position corresponding to the center of the maskpattern on the exposed material is taken as Ie (L, S). In the exposureusing a photomask (light-shielding mask) in which a completelight-shielding film is provided as a mask pattern instead of the maskenhancer of the image enhancement mask, the light intensity generated atthe position corresponding to the center of the mask pattern on theexposed material is taken as Ic (L). In the exposure using a photomask(light-transmitting mask) in which a regular light-transmitting portionis provided instead of the opening (a phase shifter having atransmittance of 1.0) of the image enhancement mask and alight-shielding portion constituted by a complete light-shielding filmis provided instead of the light-transmitting portion of the imageenhancement mask, the light intensity generated at the positioncorresponding to the center of the mask pattern on the exposed materialis taken as Io (S).

[0254] In this case, in the image enhancement mask, the intensity of themask pattern diffracted light generated at the position corresponding tothe center of the mask pattern on the exposed material corresponds to Ic(L), and the light intensity of the shifter transmitted light generatedat the position corresponding to the center of the mask pattern on theexposed material corresponds to Io (S). Therefore, the light intensityIe (L, S) can be approximated to a value obtained by converting thelight intensity Ic (L) and the light intensity Io (S) to the lightintensities in a phase space, overlapping the two light intensities, andsquaring the result. That is,

Ie (L, S)=((Ic(L))^(0.5)−(Io (S))^(0.5))².

[0255] Therefore, in the image enhancement mask, the condition thatprovides the smallest Ie (L, S), that is, the light-shielding propertymaximizing condition is:

[0256] Ic (L)=Io (S). In other words, as the light-shielding propertymaximizing condition, the mask pattern line width L and the openingwidth S that satisfy Ic (L)=Io (S) can be obtained.

[0257] FIGS. 23(a) to (c) show the simulation results of the lightintensity Ie (L, S) generated at the position corresponding to thecenter of the mask pattern on the exposed material when the mask patternline width L and the opening width S are varied in the exposure with theimage enhancement mask shown in FIG. 22, represented by contour lines ofthe light intensity with the opening width S and the mask pattern linewidth L in the vertical axis and the horizontal axis, respectively.Herein, in each of FIGS. 23(a) to (c), the graph indicating therelationship of Ic (L)=Io (S) described above is superimposed. Thesimulation results shown in FIGS. 23(a) to (c) are obtained usingdifferent exposure light sources. The simulation results shown in FIG.23(a) are obtained using regular exposure with a circular light source.The simulation results shown in FIG. 23(b) are obtained using annularexposure with an annular light source. The simulation results shown inFIG. 23(c) are obtained using quadrupole exposure with light sourcespositioned at four points on diagonal coordinates. Other simulationconditions are such that the wavelength of the exposure light λ=0.193μm, and the numerical aperture NA of the projecting optical system ofthe exposure apparatus=0.6.

[0258] As shown in FIGS. 23(a) to (c), the dependence of the lightintensity Ie (L, S) on the mask pattern line width L and the openingwidth S is slightly varied depending on the shape of the exposure lightsource, but the condition that provides the smallest light intensity Ie(L, S) can be represented accurately by the relationship of Ic (L)=Io(S), regardless of the shape of the exposure light source.

[0259]FIG. 24 is a schematic view showing the principle of the maskpattern overlapping method of the present invention regarding the caseof the image enhancement mask having a mask pattern with a square shape(the length of one side is L) constituted by a mask enhancer with anopening width S. Also in the image enhancement mask shown in FIG. 24,the light intensity of the mask pattern diffracted light generated atthe position corresponding to the center of the mask pattern on theexposed material corresponds to Ic (L), and the light intensity of theshifter transmitted light generated at the position corresponding to thecenter of the mask pattern on the exposed material corresponds to Io(S). Therefore, also in the image enhancement mask shown in FIG. 24, themask pattern line width L and the an opening width S that provide thesmallest Ie (l, S) can be obtained based on the relationship Ic (L)=Io(S).

[0260] FIGS. 25(a) to (c) show the simulation results of the lightintensity Ie (L, S) generated at the position corresponding to thecenter of the mask pattern on the exposed material when the mask patternline width L and the opening width S are varied in the exposure with theimage enhancement mask shown in FIG. 24, represented by contour lines ofthe light intensity with the opening width S and the mask pattern linewidth L in the vertical axis and the horizontal axis, respectively.Herein, in each of FIGS. 25(a) to (c), the graph indicating therelationship of Ic (L)=Io (S) described above is superimposed. Thesimulation results shown in FIGS. 25(a) to (c) are obtained usingdifferent exposure light sources. The simulation results shown in FIG.25(a) are obtained using regular exposure with a circular light source.The simulation results shown in FIG. 25(b) are obtained using annularexposure with an annular light source. The simulation results shown inFIG. 25(c) are obtained using quadrupole exposure with light sourcespositioned at four points on diagonal coordinates. Other simulationconditions are such that the wavelength of the exposure light λ=0.193μm, and the numerical aperture NA of the projecting optical system ofthe exposure apparatus=0.6.

[0261] As shown in FIGS. 25(a) to (c), the dependence of the lightintensity Ie (L, S) on the mask pattern width L and the opening width Sis slightly varied depending on the shape of the exposure light source,but the condition that provides the smallest light intensity Ie (L, S)can be represented accurately by the relationship of Ic (L)=Io (S),regardless of the shape of the exposure light source.

[0262] In other words, there is no limitation regarding the shape of themask pattern to which the mask pattern overlapping method of the presentinvention can be applied.

[0263] More specifically, the opening width that maximizes the effectivelight-shielding properties of the mask pattern in the image enhancementmask having the mask pattern with an arbitrary shape constituted by themask enhancer can be calculated as follows.

[0264] (1) The light intensity Ic (r) generated at a position rcorresponding to the vicinity of the center of a mask pattern on anexposed material is calculated in exposure using a light-shielding maskprovided with a complete light-shielding film as the mask patterninstead of the mask enhancer of the image enhancement mask.

[0265] (2) The opening width is obtained so that the intensity of lighttransmitted through the opening is equal to Ic (r), and a phase shifteris provided in the opening.

[0266] It should be noted that since the opening width cannot be largerthan the mask pattern width, when the opening width obtained by theabove-described method exceeds the mask pattern width, the entire maskpattern is used as the phase shifter. When the light-shieldingproperties are not sufficient even if the entire mask pattern is used asthe phase shifter, the size of the original mask pattern is increased,and the opening width can be obtained again by the above-describedmethod.

[0267] In the above description, mask patterns having simple shapes havebeen described, but when a mask pattern has a complex shape, the maskpattern is divided into a plurality of patterns having a simple shape,and the mask pattern overlapping method of the present invention can beapplied to each pattern. By doing this, the optimal opening width can bedetermined for each divided pattern.

[0268] As described above, in the photomask of the second embodiment,the intensity of mask pattern diffracted light is calculated, and theopening width of the mask enhancer is calculated such that the intensityof the shifter transmitted light is equal to the intensity of the maskpattern diffracted light, and thus the light-shielding properties of themask pattern can be maximized. When a mask pattern has a complex shape,the mask pattern is divided into a plurality of patterns having a simpleshape, and the opening width is calculated such that the intensity ofthe transmitted light is equal to the intensity of the diffracted lightfor each pattern, and thus the light-shielding properties throughout themask pattern can be maximized.

[0269] In the second embodiment, the shape of the opening of the maskenhancer for generating shifter transmitted light does not have to bematched to the shape of the mask pattern, unlike the shape of the phaseshifter in the first embodiment. In other words, the shape of theopening of the mask enhancer can be set to an arbitrary shape, as longas it is within the mask pattern. Furthermore, in the image enhancementof the present invention, the method of controlling shifter transmittedlight by changing the transmittance of the phase shifter in the firstembodiment can be regarded as one of the methods of controlling theshifter transmitted light by changing the size of the opening of themask enhancer in the second embodiment. That is to say, a mask patternconstituted by a phase shifter having a predetermined transmittance canbe replaced by another mask pattern in which an opening serving as aphase shifter having a transmittance higher than the predeterminedtransmittance is provided in a light-shielding film having the sameouter shape as that of the mask pattern. Speaking in a more generalizedmanner, an opening having a predetermined transmittance and apredetermined shape and size is replaced equivalently by an openinghaving a transmittance different from the predetermined transmittanceand a shape and size different from the predetermined shape and size.However, to satisfy this, it is a condition that the size of the maskpattern is about a half of λ/NA or less. It is important that theopening provided in a fine mask pattern has the same optical behavior,regardless of the shape of the opening, as long as the intensity oflight transmitted through it is the same. An effect generated when thisis utilized in the second embodiment will be described below.

[0270]FIG. 26(a) shows a semi-transparent pattern constituted by asemi-transparent film having a line width L and a transmittance T.Herein, L=0.1 μm.

[0271] FIGS. 26(b) to (d) show opening patterns obtained by providing anopening having a transmittance of 1.0 in a transparent substrate, andFIG. 26(b) shows an opening pattern in which an opening constituted byone line with a width S is provided in the center of a region with aline width L (S<L), FIG. 26(c) shows an opening pattern in whichopenings constituted by two lines with a width of S/2 are provideduniformly in a region with a line width L, and FIG. 26(d) shows anopening pattern in which square openings having an area S are providedin the center of a region having an area L.

[0272]FIG. 26(e) shows the results of evaluating the intensity of lighttransmitted through the opening at the position corresponding to thecenter of each opening pattern with simulations when the opening patternshown in each of FIGS. 26(b) to (d) is irradiated with light whilechanging the size S from 0 to L. In FIG. 26(e), using the transmittanceT (vertical axis) of a semi-transparent film at the time when theintensity of light transmitted through a semi-transparent film at theposition corresponding to the center of a semi-transparent pattern inthe case where the semi-transparent pattern shown in FIG. 26(a) isirradiated with light is equal to the light intensity at the positioncorresponding to the center of each opening pattern, the light intensityat the position corresponding to the center of each opening pattern isevaluated. In FIG. 26(e), the light intensity at the positioncorresponding to the center of each opening pattern is plotted as afunction using the opening area ratio S/L (horizontal axis) as theparameter.

[0273] As shown in FIG. 26(e), the dependence of the transmittance T ofthe semi-transparent film in the semi-transparent pattern equivalent toeach opening pattern (hereinafter, referred to as “equivalenttransmittance T) on the opening area ratio S/L is slightly varieddepending on the shape of each opening pattern, but there is a strongcorrelation between the equivalent transmittance T and the opening arearatio S/L in all the opening patterns.

[0274]FIG. 27(a) shows the results of evaluating the intensitydistribution of light transmitted through the semi-transparent film withsimulations in which the transmittance T is 0.5, when thesemi-transparent pattern shown in FIG. 26(a) is irradiated with light.In FIG. 27(a), the position 0 (the original point in the horizontalaxis) corresponds to the center of the semi-transparent pattern. FIG.27(a) also shows the simulation results of the focus characteristics ofthe light intensity distribution. The focus characteristics areevaluated regarding the best focus position and the position defocusedfrom the best focus position by 0.15, 0.30 and 0.45 μm.

[0275] FIGS. 27(b) to (d) show the results of evaluating the intensitydistribution of light transmitted through an opening with simulations inwhich the equivalent transmittance T is 0.5, when the opening patternshown in each of FIGS. 26(b) to (d) is irradiated with light. In thiscase, as seen from FIG. 26(e), S in the opening pattern shown in FIG.26(b) is 0.068 μm, S in the opening pattern shown in FIG. 26(c) is 0.070μm, and S in the opening pattern shown in FIG. 26(d) is 0.069 μm(however, L is 0.10 μm in all the cases). In FIGS. 27(b) to (d), theposition 0 (the original point in the horizontal axis) corresponds tothe center of each opening pattern. FIG. 27(b) to (d) also show thesimulation results of the focus characteristics of the light intensitydistribution. The focus characteristics are evaluated regarding the bestfocus position and the position defocused from the best focus positionby 0.15, 0.30 and 0.45 μm.

[0276] FIGS. 27(b) to (d) indicate that if the light intensities at theposition corresponding to its center in each opening pattern arematched, the optical characteristics thereof are totally equal.

[0277] In the image enhancement of the present invention in which themask pattern diffracted light is cancelled by the shifter transmittedlight, it is sufficient to adjust only the effective intensity of theshifter transmitted light, and the method that can be most easilyrealized can be selected as the method for generating the shiftertransmitted light, as long as its intensity is the same.

[0278] Furthermore, if the opening area ratio is the same, thedependence of the intensity of the shifter transmitted light transmittedthrough the opening on the opening shape is small, and although notstrictly, but practically, the intensity of the shifter transmittedlight can be substantially uniquely determined by the opening arearatio.

[0279] For example, as shown in FIG. 26(e), the dependence of theequivalent transmittance T of each opening pattern shown in FIGS. 26(b)to (d) on the opening area ratio S/L can be represented approximatelyby:

T=1.45×(S/L)−0.45

[0280] This approximation is quite accurate with respect to atransmittance of 0.2 or more, although it is not accurate with respectto a low transmittance of 0.1 or less. However, in the above equation,the coefficient (1.45) of (S/L) and the constant (0.45) are changeddepending on the wavelength of the exposure light or the mask patternsize.

[0281] Therefore, in the photomask of the second embodiment, the openingshape in the mask pattern can be changed to an arbitrary shape withinthe range in which the opening area ratio can be kept constant. Forexample, in the case where a mask pattern is to be formed for practicaluse, in view of the degree of attachment between the light-shieldingfilm and the substrate, it is not preferable that an extremely narrowlight-shielding film is produced. In this case, for example, the openingis divided into regions, each of which has a radius λ/NA or less,without changing its opening area ratio so as to ensure that a narrowlight-shielding film is not present alone.

[0282] In the second embodiment, in order to maximize the effectivelight-shielding properties of a mask pattern in view of the principle ofthe image enhancement of the present invention, the opening width S canbe determined based on the relationship Ic (L)=Io (S). However, if it issufficient to make the effective light-shielding properties of the maskpattern higher than those of the mask pattern constituted by a completelight-shielding film, the opening width S may be determined such thatthe relationship Ic (L)=Io (S) is almost satisfied.

[0283] More specifically, as described above, the light intensity Ie (L,S) generated at the position corresponding to the center of the maskpattern on the exposed material through the image enhancement maskhaving the mask pattern with a line width L constituted by the maskenhancer having an opening width S can be estimated using therelationship:

Ie (L, S)=((Ic (L))^(0.5)−(Io (S))^(0.5))²,

[0284] where Ic (L) is the light intensity of the mask patterndiffracted light and Io(S) is the light intensity of the shiftertransmitted light). Therefore, the condition in which the shiftertransmitted light becomes excessive, and the effective light-shieldingproperties of the mask pattern are deteriorated to be equal to those ofthe mask pattern constituted by a complete light-shielding film can beIe (L, S)=Ic (L), that is,

−((Ic(L))⁰ ⁵−(Io (S))^(0.5))=(Ic(L))^(0.5).

[0285] In this case, since

(Io (S))^(0.5)=2×(Ic(L))^(0.5)

[0286] is satisfied, and therefore

Io (S)=4×(Ic(L))

[0287] is satisfied. In other words, when the light intensity of theshifter transmitted light reaches four times the light intensity of themask pattern diffracted light, the effective light-shielding propertiesof the mask pattern becomes equal to those of the mask patternconstituted by a complete light-shielding film. In other words, when theopening width S is set so that the light intensity of the shiftertransmitted light is not more than four times the light intensity of themask pattern diffracted light, the effective light-shielding propertiesof the mask pattern can be improved from the mask pattern constituted bya complete light-shielding film.

[0288] In the second embodiment, for more generalized situations, theopening width can be determined in the following manner. To reduce thelight intensity Ih generated at the position corresponding to the centerof the mask pattern on an exposed material to 1/D of the intensity Ic ofthe mask pattern diffracted light, the opening width that satisfies thefollowing inequality can be used.

−((Ic)^(0.5)−(Io)^(0.5))<(Ic/D)^(0.5)

<((Ic)^(0.5)−(Io)^(0.5))

[0289] More specifically, in the case of D=3, the opening width is setso that Io (light intensity of the shifter transmitted light) is between0.18 times and 2.5 times the value of Ic. In the case of D=5, theopening width is set so that Io is between 0.31 times and 2.1 times thevalue of Ic. In the case of D=10, the opening width is set so that Io isbetween 0.48 times and 1.7 times the value of Ic. It is not necessary tomaximize the light-shielding properties of all the mask patterns forpractical use, so that if the opening width is set so that Io is betweenabout ⅓ and 2 times the value of Ic, the light-shielding properties ofthe mask pattern can be improved sufficiently.

[0290] Furthermore, in a method for forming a pattern of the secondembodiment, that is, a method for forming a pattern using the photomaskof the second embodiment, a positive resist film or a negative resistfilm can be used as the resist film. When a positive resist film isused, a resist pattern having a mask pattern shape can be formed bydeveloping the positive resist film irradiated with exposure light, andremoving portions other than the portion corresponding to the maskpattern in the positive resist film. When a negative resist film isused, a resist pattern having an opening with a mask pattern shape canbe formed by developing the negative resist film irradiated withexposure light, and removing the portion corresponding to the maskpattern in the negative resist film. Regardless of whether the positiveresist film is used or the negative resist film is used, when the maskpattern width L is smaller than about 0.4×λ/NA, the precision of thesize of the resist pattern can be improved significantly, compared withthe conventional methods.

[0291] Variation Example of the Second Embodiment

[0292] Hereinafter, a photomask according to a second embodiment of thepresent invention, a method for producing the same and a method forforming a pattern using the photomask will be described with referenceof the accompanying drawings.

[0293] A variation example of the second embodiment is different fromthe second embodiment in the following aspects. In the secondembodiment, it is implicitly assumed that a light-shielding portionconstituting a mask pattern constituted by a mask enhancer is a completelight-shielding film. However, in this variation example of the secondembodiment, a semi-light-shielding portion having a predeterminedtransmittance with respect to exposure light is used as thelight-shielding portion constituting the mask pattern. It is ideal thatthis semi-light-shielding portion does not generate a phase differencebetween this portion and a light-transmitting portion with respect toexposure light, but if the phase difference is (−30+360×n) degrees ormore and (30+360×n) degrees or less (n=an integer), it is regarded asbeing able to be ignored.

[0294] In the variation example of the second embodiment, the principleof the image enhancement is basically the same as in the case of FIG. 3,but slightly different effects result. Hereinafter, effects provided byusing the semi-light-shielding portion as the light-shielding portionconstituting the mask pattern will be described with reference to FIGS.28 and 29. FIG. 28 is a schematic view showing the principle of theimage enhancement of the present invention in the case where the linewidth L of the mask pattern constituted by the mask enhancer issufficiently small, that is, smaller than 0.8×λ/NA (λ is the wavelengthof the exposure light and NA is the numerical aperture). FIG. 29 is aschematic view showing the principle of the image enhancement of thepresent invention in the case where the line width L of the mask patternconstituted by the mask enhancer is sufficiently large, that is largerthan 0.8×λ/NA.

[0295] As shown in FIGS. 28 and 29, the image enhancement mask has astructure in which the semi-light-shielding mask provided with thesemi-light-shielding portion corresponding to the mask pattern of theimage enhancement mask and a phase shift transmitted mask provided witha phase shift pattern corresponding to the phase shifter of the imageenhancement mask in a complete light-shielding portion covering thesurface of the mask are overlapped. FIGS. 28 and 29 also show theamplitude intensity of the light transmitted through each of thesemi-light-shielding mask, the phase shift transmitted mask and theimage enhancement mask and transferred at the position corresponding toline AA′.

[0296] First, as shown in FIG. 28, when the line width L of the maskpattern constituted by a mask enhancer is smaller than 0.8×λ/NA and thesemi-light-shielding portion is used as the light-shielding portion, theprinciple of the image enhancement is substantially the same as in thecase of FIG. 3(a) using a complete light-shielding portion as thelight-shielding portion. However, as seen in the amplitude intensity ofthe light transmitted through the semi-light-shielding mask, theintensity transferred at the position corresponding to the center of thesemi-light-shielding pattern constituted by the semi-light-shieldingportion results from not only the light from the periphery of thesemi-light-shielding pattern, but also from the light transmittedthrough the inner portion of the semi-light-shielding pattern.Therefore, the light intensity transferred at the position correspondingto the center of the semi-light-shielding pattern shown in FIG. 28 isincreased from when a complete light-shielding portion is used as thelight-shielding portion by the extent of the light transmitted throughthe inner portion of the semi-light-shielding pattern. Therefore, inorder to cancel this increase, it is necessary to make the width of thephase shifter larger than when a complete light-shielding portion isused as the light-shielding portion. Only this point is differentbetween when the semi-light-shielding portion is used as thelight-shielding portion and when a complete light-shielding portion isused as the light-shielding portion in the case where the line width Lof the mask pattern is smaller than 0.8×λ/NA.

[0297] When the line width of the complete light-shielding patternconstituted by the complete light-shielding portion becomes larger than0.8×λ/NA, there is almost no light going into the back side of the maskpattern from the periphery of the pattern, so that the light intensitytransferred at the position corresponding to the center of the completelight-shielding pattern is substantially 0. Therefore, in the case wheresuch a phase shifter is arranged in the complete light-shieldingpattern, the contrast is reduced, however small the width of the phaseshifter is.

[0298] On the other hand, as shown in FIG. 29, when the line width L ofthe mask pattern constituted by the mask enhancer is larger than0.8×λ/NA and the semi-light-shielding portion is used as thelight-shielding portion, there is light transmitted through thesemi-light-shielding pattern of the semi-light-shielding maskcorresponding to the image enhancement mask, however larger than0.8×λ/NA the line width L becomes. Therefore, the light intensitytransferred at the position corresponding to the center of thesemi-light-shielding pattern never becomes 0. Therefore, the contrast isnot reduced, regardless of the position in the semi-light-shieldingpattern at which the phase shifter is arranged, as long as the phaseshifter has a size and width that can transmit light having an intensityjust as high so as to cancel the light transmitted through thesemi-light-shielding pattern at this point. Furthermore, when the linewidth L of the mask pattern is larger than a value twice 0.8×λ/NA, aplurality of phase shifters can be arranged, as long as the phaseshifters have the above-described size and width and are arranged apartfrom each other by 0.8×λ/NA or more.

[0299] Next, advantages provided when producing a mask by using thesemi-light-shielding portion as the light-shielding portion constitutinga mask pattern in the image enhancement mask instead of the completelight-shielding portion will be described.

[0300]FIG. 30(a) is a plan view of a photomask provided with a completelight-shielding pattern with a line width L constituted by a completelight-shielding portion and shows the light intensity of lighttransmitted through the mask and transferred at the positioncorresponding to the line AA′. FIG. 30(b) is a plan view of a photomaskprovided with a semi-light-shielding pattern with a line width Lconstituted by a semi-light-shielding portion and shows the lightintensity of light transmitted through the mask and transferred at theposition corresponding to the line AA′.

[0301] When the line width L of the complete light-shielding patternbecomes larger than 0.8×λ/NA, as shown in FIG. 30(a), the intensity ofthe light transferred at the position corresponding to the center of thecomplete light-shielding pattern becomes 0. In other words, when thecomplete light-shielding portion is used as the light-shielding portionconstituting the mask pattern in the image enhancement mask, as shown inFIG. 30(c), the width of the phase shifter is reduced as the width L ofthe complete light-shielding pattern is increased, and it is necessaryto eliminate the phase shifter when the line width L becomes larger than0.8×λ/NA However, when actually producing a mask pattern, the line widthof the phase shifter is changed by unit of a mask grid (the minimumwidth by which the mask size can be adjusted: generally about 1 nm), andthe minimum of the line width of the phase shifter that can be producedis limited, because of limitations in terms of mask processing.Therefore, if the complete light-shielding portion is used as thelight-shielding portion constituting the mask pattern in the imageenhancement mask, it is not always possible to arrange an optical phaseshifter in the light-shielding pattern.

[0302] On the other hand, as shown in FIG. 30(b), even if the line widthof the semi-light-shielding pattern is larger than 0.8×λ/NA, the lightintensity corresponding to the center of the semi-light-shieldingpattern never becomes 0, and there is residual light intensity resultingfrom the light transmitted through the semi-light-shielding pattern. Inother words, a phase shifter can be arranged in a semi-light-shieldingpattern with any line width, as long as the phase shifter has a linewidth that can matched to this residual light intensity. Morespecifically, as shown in FIG. 30(d), the line width of the phaseshifter is decreased as the line width L of the semi-light-shieldingpattern is increased, but when the line width of the phase shifter isdecreased to a size that matches to the residual light intensity, it isnot necessary to decrease the line width of the phase shifter any more.Thus, when the semi-light-shielding portion is used as thelight-shielding portion constituting the mask pattern in the imageenhancement mask, the phase shifter having a predetermined line widthcan be arranged at an arbitrary position in the semi-light-shieldingpattern. Therefore, if the transmittance of the semi-light-shieldingportion is adjusted such that the residual light intensity of thesemi-light-shielding portion corresponds to the minimum value of thephase shifter that can be produced on an actual mask, an optimal phaseshifter can be arranged in an arbitrary semi-light-shielding pattern.Furthermore, if the transmittance of the semi-light-shielding portion atthis point is low so that a resist is not exposed to light, in thesemi-light-shielding pattern with a line width of 0.8×λ/NA or more, itcan be determined arbitrarily whether the phase shifter is arranged oreliminated. Furthermore, if the distance between the phase shifters is0.8×λ/NA or more in the semi-light-shielding pattern, a plurality ofphase shifters can be arranged in the semi-light-shielding pattern. Inthis case, if the phase shifters are arranged not in the centralportion, but in the fringe of the semi-light-shielding pattern, thecontrast in the fringe of the semi-light-shielding pattern can beemphasized.

[0303] As described above, according to the variation example of thesecond embodiment, the semi-light-shielding portion is used as thelight-shielding portion constituting the mask pattern constituted by themask enhancer, instead of the complete light-shielding portion, so thatthe arrangement of the phase shifter emphasizing the contrast of thelight intensity by the mask pattern can be realized accurately withrespect to an arbitrary pattern shape. Furthermore, the lighttransmitted through the semi-light-shielding portion constituting themask pattern makes it possible to arrange the phase shifter at anarbitrary position in the mask pattern, so that a special effect ofsetting a location at which the contrast is emphasized at an arbitraryposition in the mask pattern by arranging the phase shifter can beobtained.

[0304] In the variation example of the second embodiment, it ispreferable that the transmittance of the semi-light-shielding portionused as the light-shielding portion constituting the mask patternconstituted by the mask enhancer is about 15% or less. The reason forthis is as follows. When the light intensity Ith is the criticalintensity at which a resist film is exposed to light and the intensityIb is the background intensity of the light transmitted through thesemi-light-shielding portion, then the higher Ith/Ib leads to the lesspossibility of a reduction of the thickness of the resist film duringformation of a pattern, and it is more preferable that this value is ashigh as possible. In general, it is preferable that Ith/Ib is 2 or more.However, since Ith/Ib is decreased as the transmittance of thesemi-light-shielding portion is increased, so that it is not preferablethat the transmittance of the semi-light-shielding portion is too highfor improvement of Ith/Ib. More specifically, it is preferable that thetransmittance of the semi-light-shielding portion is 15% or less,because Ith/Ib becomes smaller than 2 when the transmittance of thesemi-light-shielding portion is about 15%.

[0305] Third Embodiment

[0306] A method for forming a pattern according to a third embodiment ofthe present invention will be described with reference to theaccompanying drawings, by taking an example a method for improving afocus margin by exposure using the photomask (an example of thephotomask according to the second embodiment) having a mask patternconstituted by the mask enhancer. The effect of improving focus marginin the third embodiment can be realized by combining the imageenhancement of the present invention in which the mask patterndiffracted light is cancelled by the shifter transmitted light and amethod for exposure. In addition, it can be considered that increasingand decreasing the opening width of the mask enhancer in the photomaskof the second embodiment has the same effect as increasing anddecreasing the transmittance of the phase shifter in the photomask ofthe first embodiment. In other words, the method for forming a patternaccording to the third embodiment can be realized by using either one ofthe photomasks according to the first or the second embodiment.

[0307] FIGS. 31(a) to (g) are diagrams explaining the dependence of thelight intensity distribution generated on an exposed material byexposure with the mask enhancer on the exposure light incident directionfrom the light source to the photomask (hereinafter, referred to simplyas “exposure light incident direction). More specifically, thesedrawings show the results of simulations performed in order to evaluatewhat influence the exposure light incident direction can give to theprofile shape of the light intensity distribution formed by cancelingthe mask pattern diffracted light by the shifter transmitted light. Morespecifically, the light intensity distribution transferred on an exposedmaterial by the exposure light using a linear mask enhancer (maskpattern width L and opening width S) provided parallel to and along theY axis of the light source coordinate as shown in FIG. 31(a) isevaluated by calculations with simulations with respect to variousexposure light incident directions.

[0308] FIGS. 31(b) to (d) show the positions at which small lightsources are arranged in the light source coordinate used in thesimulations, and FIG. 31(b) shows a light source that is incident fromthe center of the light source coordinate (vertical incident). FIG.31(c) shows a light source that is incident obliquely from the X axisdirection or the Y axis direction of the light source coordinate. FIG.31(d) shows a light source that is incident obliquely from the 45 degreedirection (straight direction of Y=X or Y=−X) of the light sourcecoordinate. The light sources shown in FIGS. 31(b) to (d) are circularlight sources having a radius of 0.05 in the light source coordinate.However, all the values on the light source coordinate are normalized bythe numerical number NA of the reduced size optical system of theexposure apparatus.

[0309] FIGS. 31(e) to (g) show the light intensity distributiongenerated at the position corresponding to the X axis of FIG. 31(a) onan exposed material by the exposure with various structures of the maskpattern. In FIGS. 31(e) to (g), 0 at the horizontal axis (position) is aposition corresponding to the center of the mask pattern.

[0310] Herein, FIG. 31(e) shows the light intensity distribution in thecase where the entire mask pattern with a width L of 0.12 μm isconstituted by a light-shielding film (S=0.0 μm) with respect to eachexposure light incident direction. However, the optical conditions otherthan the exposure light incident direction are all common, such as thewavelength of the exposure light=193 nm and the numerical aperture=0.6.

[0311] As shown in FIG. 31(e), the effective light-shielding propertiesof the mask pattern is varied by the exposure light incident direction,and the light-shielding properties in the case of oblique incidence fromthe 45 degree direction are worst.

[0312]FIG. 31(f) shows the light intensity distribution in the casewhere the mask pattern width L is adjusted such that the lightintensities at the position 0 on the light intensity distribution shownin FIG. 31(e) are matched with respect to the exposure light incidentdirections.

[0313]FIG. 31(g) shows the light intensity distribution in the casewhere an opening (width S) serving as a phase shifter is provided by theimage enhancement of the present invention such that the effectivelight-shielding properties of the mask pattern with an adjusted width Las shown in FIG. 31(f) are maximized with respect to the exposure lightincident directions. Here, in order to observe what influence occurs inthe profile shape of the light intensity distribution by canceling themask pattern diffracted light with the shifter transmitted light, thelight intensities of each of the shifter transmitted light and the maskpattern diffracted light at the arrangement positions of the lightsources shown in FIG. 31(b) to (d) are made the same and evaluation isperformed. Furthermore, the scale on the vertical axis (light intensity)of FIG. 31(g) is offset by 0.1 so that the profiles of the lightintensity distributions shown in FIG. 31(f) and 31(g) can be comparedeasily.

[0314] When the profile shapes of the light intensity distributionsshown in FIGS. 31(f) and 31(g) are compared regarding the case where theexposure light incident direction is the direction from the center ofthe light source coordinate, the profile shape of the light intensitydistribution becomes flat at the position corresponding to the center ofthe mask pattern by canceling the mask pattern diffracted light with theshifter transmitted light. This means that the light-shieldingproperties of the mask pattern are improved, whereas the profile shapeof the light intensity distribution becomes dull (deteriorate).

[0315] When the profile shapes of the light intensity distributionsshown in the FIGS. 31(f) and 31(g) are compared regarding the obliqueincidence where the exposure light incident direction is the obliqueincidence from the X axis direction or the Y axis direction of thelight, the profile shape of the light intensity distribution is notsubstantially changed even if the mask pattern diffracted light iscancelled by the shifter transmitted light.

[0316] On the other hand, when the profile shapes of the light intensitydistributions shown in FIGS. 31(f) and 31(g) are compared regarding thecase where the exposure light incident direction is the obliqueincidence from the 45 degree direction of the light source coordinate,the profile shape of the light intensity distribution becomes sharp(improved) at the position corresponding to the center of the maskpattern by canceling the mask pattern diffracted light with the shiftertransmitted light.

[0317] In other words, by using the image enhancement of the presentinvention of canceling the mask pattern diffracted light with theshifter transmitted light, the light-shielding properties at theposition corresponding to the center of the mask pattern can bemaximized with respect to any exposure light incident direction.However, the influence on the profile shape of the light intensitydistribution is varied depending on the exposure light incidentdirection.

[0318] Hereinafter, a method for improving the focus characteristics inthe formation of a pattern by exposure using the mask enhancer,utilizing the fact that the profile shape of the light intensitydistribution is not degraded when the oblique incidence from the 45degree direction is used as the exposure light incident direction in theimage enhancement of the present invention will be described.

[0319] FIGS. 32(a) to (d) and FIG. 33(a) to (d) are graphs showing theprinciple of a method for improving the defocus characteristicsutilizing a mask enhancer. All the calculation result shown in FIGS.32(a) to (d) and FIGS. 33(a) to (d) are simulation results using obliqueincident exposure (off-axis illumination) from the 45 degree directionsof the light source coordinate shown in FIG. 31(d).

[0320]FIG. 32(a) shows the light intensity distribution projected on anexposed material in the exposure using the photomask provided with asingle light-shielding film with a width L and a single opening with awidth S. FIG. 32(a) shows the results in the case of L=0.15 μm, and theresults when S is varied to 0.045 μm, 0.060 μm, 0.075 μm, and 0.090 μm.In FIG. 32(a), 0 in the horizontal axis (position) is the positioncorresponding to the center of the light-shielding film or the center ofthe opening on the exposed material.

[0321]FIG. 32(b) shows changes of the light intensity at the positioncorresponding to the center of the light-shielding film or the center ofthe opening in the light intensity distribution shown in FIG. 32(a) withrespect to defocusing in the exposure.

[0322] As shown in FIG. 32(b), the light intensity generated by thelight-shielding film increases as defocusing increased, whereas thelight intensity generated by the opening decreases as defocusingincreased.

[0323] In the case where the mask pattern diffracted light and theshifter transmitted light are desired to interfere each other as lightswith opposite phases by producing a mask enhancer structure in which anopening serving as a phase shifter is provided in a light-shieldingfilm, the light intensity realized by the mask enhancer is proportionalto a difference between the mask pattern diffracted light and theshifter transmitted light. In this case, if the light intensity of theshifter transmitted light is set to be larger than the light intensityof the mask pattern diffracted light in the best focus (defocus is 0),the difference in the light intensity between the two lights decreasesas the defocus increases, and the difference in the light intensityreaches 0 at a certain amount of defocus, and thereafter the lightintensity of the mask pattern diffracted light becomes larger than theshifter transmitted light and the difference in the light intensityincreases as the defocus increases.

[0324] In the third embodiment, utilizing this effect, the defocuscharacteristics can be improved. For example, the light intensity at theposition corresponding to the center of a mask pattern on an exposedmaterial in exposure using a photomask provided with a mask pattern witha pattern width L (L=0.15 μm) constituted by a mask enhancer with anopening width S (S=0.045 μm, 0.060 μm, 0.075 μm, and 0.090 μm) can beobtained by adding the light intensity generated by the light-shieldingfilm and the light intensity generated by the opening in a phase space,as shown in FIG. 32(b). In this case, first, the light intensity on thephase space by generated by each of the light-shielding film and theopening can be obtained by taking the square root of each lightintensity. Furthermore, a negative value is used as the light intensityon the phase space generated by the opening serving as a phase shifterin view of the phase.

[0325]FIG. 32(c) shows changes of the light intensity on the phase spacegenerated by each of the light-shielding film and the opening obtainedin the above-described manner with respect to defocusing in theexposure.

[0326]FIG. 32(d) shows changes of the total value of the lightintensities on the phase space generated by the light-shielding film andthe opening shown in FIG. 32(c). The results shown in FIG. 32(d) showsthe defocus characteristics of the light intensity (on a phase space) atthe position corresponding to the center of a mask pattern on an exposedmaterial in exposure using a photomask provided with a mask pattern witha pattern width L (L=0.15 μm) constituted by a mask enhancer with anopening width S (S=0.045 μm, 0.060 μm, 0.075 μm, and 0.090 μm).

[0327] As shown in FIG. 32(d), in the case of an opening width S=0.06μm, the mask pattern diffracted light and the shifter transmitted lightare completely cancelled each other in the best focus, and therefore thelight intensity (on the phase space) at the position corresponding tothe center of the mask pattern is substantially 0. On the other hand,when the opening width S becomes 0.06 μm or more, the shiftertransmitted light becomes excessive in the best focus, so that the lightintensity (on the phase space) at the position corresponding to thecenter of the mask pattern has a negative value. However, even if theshifter transmitted light becomes excessive in the best focus, the maskpattern diffracted light is changed to be excessive as the defocusincreases.

[0328]FIG. 33(a) shows changes of the light intensities (correspondingto energy intensity) on the actual space obtained by squaring the lightintensity on the phase space shown in FIG. 32(d) with respect to defocusin exposure. In other words, the results shown in FIG. 33(a) shows thedefocus characteristics of the light intensity (on the actual space) atthe position corresponding to the center of a mask pattern on an exposedmaterial in the exposure using a photomask provided with a mask patternwith a pattern width L (L=0.15 μm) constituted by a mask enhancer withan opening width S (S=0.045 μm, 0.060 μm, 0.075 μm, and 0.090 μm).

[0329] As shown in FIG. 33(a), in the case of the mask enhancer in whichthe shifter transmitted light becomes excessive in the best focus, theeffective light-shielding properties are maximized in the best focusstate. In this case, even if the effective light-shielding propertiesare not maximized in the best focus and if the effective light-shieldingproperties are in the range that causes no practical problems, thepossibility of the degradation of the light-shielding properties due todefocusing is reduced by the extent that the focus position at which thelight-shielding properties is maximized is shifted to the defocusposition. This is the principle of a method for improving the defocuscharacteristics utilizing the mask enhancer in the third embodiment.

[0330]FIG. 33(b) shows the light intensity distribution projected on anexposed material in the case where the mask enhancer with each openingwidth S described above is used at the best focus. As shown in FIG.33(b), regardless of whether the shifter transmitted light is optimal orexcessive, the light intensity distribution having substantially equalcontrast can be realized with respect to each opening width S. In otherwords, sufficient light-shielding properties are realized with respectto all the opening widths S.

[0331]FIG. 33(c) shows the light intensity distribution projected on anexposed material in the case where a mask enhancer with an opening widthS of 0.09 μm is used at various focus positions. As shown in FIG. 33(c),according to this mask enhancer, although the light intensitydistribution at the position corresponding to the outside of the maskpattern region is changed by defocusing, the light intensitydistribution at the position corresponding to the inside of the maskpattern region is substantially not changed by defocusing. Forreference, FIG. 33(d) shows the light intensity distribution projectedon an exposed material in the case where a complete light-shielding filmis used at various focus positions instead of the mask enhancer.

[0332] As described above, according to the third embodiment, utilizingthe action of the mask enhancer to control the shifter transmitted lightwith respect to the mask pattern diffracted light, the shiftertransmitted light is set to be excessive with respect to the maskpattern diffracted light, so that the defocus characteristics in thelight intensity distribution can be improved, and therefore the focusmargin in pattern formation can be improved drastically.

[0333] In the third embodiment, when setting the shifter transmittedlight to be excessive with respect to the mask pattern diffracted light,if a condition that the light-shielding properties should not be lowerthan those of a mask pattern constituted by a complete light-shieldingfilm is set, the light intensity of the shifter transmitted light at theposition corresponding to the center of the mask pattern should not beat least four times larger than the light intensity distribution of themask pattern diffracted light at the position corresponding to thecenter of the mask pattern. In other words, this condition defines theupper limit with respect to the opening width of the mask enhancer (withrespect to the transmittance when the transmittance of the phase shifteris adjusted to control the shifter transmitted light).

[0334] In the above, referring to FIGS. 32(a) to (d) and FIGS. 33(a) to(d), the principle of a method for improving the defocus characteristicsutilizing a mask enhancer has been described. When forming the lightintensity distribution by synthesizing the mask pattern diffracted lightand the shifter transmitted light as described above, the profile shapeis affected significantly by the exposure light incident direction (seeFIG. 31(g)). Therefore, the influence of the exposure light incidentdirection on the method for improving the defocus characteristicsutilizing a mask enhancer will be described below.

[0335] FIGS. 34(a) to (c), FIGS. 35(a) to (c) and FIGS. 36(a) to (c) aregraphs explaining the dependence of the profile shape change of thelight intensity distribution by defocusing on the exposure lightincident direction. More specifically, FIGS. 34(a) to (c), FIGS. 35(a)to (c) and FIGS. 36(a) to (c) show the results of the defocuscharacteristics of the mask enhancer in which the light-shieldingproperties with respect to each of the exposure light incidentdirections are maximized as shown in FIG. 31(g), which are obtained bysimulations, using the exposure light incident directions shown in FIGS.31(b) to (d). The results shown in FIGS. 34(a) to (c) are resultsobtained at the time when the exposure light is incident from thedirection from the center of the light source coordinate. The resultsshown in FIGS. 35(a) to (c) are results obtained at the time when showsthe exposure light is incident obliquely from the X axis direction orthe Y axis direction of the light source coordinate. The results shownin FIGS. 36(a) to (c) are results obtained at the time when the lightsource is incident obliquely from the 45 degree direction of the lightsource coordinate. The results shown in FIG. 34(a), FIG. 35(a), and FIG.36(b) show the defocus characteristics of the light intensitydistribution when the mask enhancer is replaced by a light-shieldingfilm having the same outer size (that is, the light intensitydistribution by the mask pattern diffracted light). FIG. 34(b), FIG.35(b), and FIG. 36(c) show the defocus characteristics of the lightintensity distribution when an opening having the same size as theopening of the mask enhancer is provided in the light-shielding film(that is, the light intensity distribution by the shifter transmittedlight). FIG. 34(c), FIG. 35(c), and FIG. 36(c) show the defocuscharacteristics of the light intensity distribution when the maskenhancer is used (that is, the light intensity distribution by thesynthesized light of the mask pattern diffracted light and the shiftertransmitted light). Here, the scales on the vertical axis (lightintensity) of FIGS. 34(c), 35(c), and 36(c) are offset by 0.1 so thatthe results of FIGS. 34(c), 35(c), and 36(c) can be compared with theresults shown in other drawings easily.

[0336] As shown in FIGS. 34(b), 35(b), and 36(b), the defocuscharacteristics of the light intensity distribution by the shiftertransmitted light has dependence on the exposure light incidentdirection, but the difference in the defocus characteristicscorresponding to each exposure light incident direction is not verylarge. However, as shown in FIGS. 34(a), 35(a), and 36(a), the defocuscharacteristics of the light intensity distribution by the mask patterndiffracted light are significantly varied with the exposure lightincident direction. In particular, when the exposure light is incidentfrom the direction from the center of the light source coordinate, theprofile is such that the light intensity at the position correspondingto the vicinity of the center of the mask pattern increases locally bydefocusing. Therefore, when the exposure light is incident from thedirection from the center of the light source coordinate and the shiftertransmitted light is added to the mask pattern diffracted light, thenthis profile is deteriorated further. In reality, when comparing thedefocus characteristics of the profile shape of the light intensitydistribution shown in FIG. 34(a) with the defocus characteristics of theprofile shape of the light intensity distribution shown in FIG. 34(c),the profile shape of the light intensity distribution by the maskenhancer is deteriorated by defocusing. On the other hand, when theexposure light is incident obliquely from the X axis direction or the Yaxis direction of the light source coordinate, as shown in FIGS. 35(a)to (c), even if the shifter transmitted light is added to the maskpattern diffracted light, the profile shape of the light intensitydistribution is not deteriorated nor improved. When the exposure lightis incident obliquely from the 45 degree directions of the light sourcecoordinate, as shown in FIGS. 36(a) to (c), when the shifter transmittedlight is added to the mask pattern diffracted light, the profile shapeof the light intensity distribution is improved.

[0337] For clarification of the above-described results, the inventor ofthe present invention calculated the DOF (depth of focus)characteristics at the time when exposure is performed from eachexposure light incident direction, using a photomask whose openingserving as the phase shifter in the mask enhancer has a different sizewith simulations. FIGS. 37(a) to (c) show the results thereof FIG. 37(a)shows the results obtained at the time when the exposure light isincident from the direction from the center of the light sourcecoordinate. FIG. 37(b) shows the results obtained at the time when showsthe exposure light is incident obliquely from the X axis direction orthe Y axis direction of the light source coordinate. FIG. 37(c) showsthe results obtained at the time when the light source is incidentobliquely from the 45 degree direction of the light source coordinate.Here, a mask enhancer having an opening width adjusted such that thelight-shielding properties are maximized with respect to each exposurelight incident direction (hereinafter, referred to as an optimal openingwidth), a mask enhancer having an opening width smaller than the optimalopening width, and a mask enhancer having an opening width larger thanthe optimal opening width were used as the mask enhancer. Forcomparison, the DOF characteristics at the time when the mask enhanceris replaced by a complete light-shielding film having the same outershape were also calculated with simulations. The DOF characteristics areevaluated based on the change of a pattern size by defocusing when anexposure energy for providing a size of a pattern (resist pattern)formed at the best focus of 0.12 μm is set. In FIGS. 37(a) to (c), Ldenotes a mask pattern width, S denotes an opening width, and the focusposition (horizontal axis) 0 corresponds to the best focus position.

[0338] As shown in FIG. 37(a), when the exposure light is incident fromthe center of the light source coordinate, the DOF characteristics aredeteriorated as the opening width of the mask enhancer increases, andthe DOF characteristics at the time when a complete light-shielding filmis used as the mask pattern (L/S=0.12/0 μm) are best.

[0339] On the other hand, as shown in FIG. 37(b), when the exposurelight is incident obliquely from the X axis or the Y axis of the lightsource coordinate, the DOF characteristics do not depend on the openingwidth of the mask enhancer, and the DOF characteristics are the same,regardless of whether the mask enhancer is used or a completelight-shielding film is used (L/S=0.13/0 μm).

[0340] However, as shown in FIG. 37(c), when the exposure light isincident obliquely from the 45 degree directions of the light sourcecoordinate, the DOF characteristics are improved as the opening width ofthe mask enhancer increases, and the DOF characteristics at the timewhen a complete light-shielding film is used as the mask pattern(L/S=0.12/0 μm) are worst.

[0341] Thus, in order to improve the defocus characteristics of thelight intensity distribution generated by interference of the maskpattern diffracted light and the shifter transmitted light in theobliquely incidence exposure from the 45 degree directions, it ispreferable to increase the shifter transmitted light as high as possiblein the range in which the minimum and necessary effectivelight-shielding properties can be achieved.

[0342] In the above, a method for improving the defocus characteristicsby the mask enhancer in the obliquely incidence exposure from the 45degree directions has been described, and next a method for setting alight source position that can realize the effect of improving thedefocus characteristics in reality will be described.

[0343] FIGS. 38(a) to (c) are diagrams showing a DOF maps correspondingto various light source positions in exposure using a mask patternconstituted by a complete light-shielding film. Mores specifically, alinear mask pattern parallel to the Y axis on the light sourcecoordinate as shown in FIG. 38(a) is assumed as the mask pattern forevaluating the DOF map. As the light source position, that is, theexposure light incident direction, positions of the light sourcessymmetric with respect to the X axis and the Y axis on the coordinate ofthe light source and four rotational symmetric as shown in FIG. 38(b)are assumed so that the DOF map corresponding to the linear mask patternparallel to the X axis on the light source coordinate exhibit the samecharacteristics as those of the mask pattern shown in FIG. 38(a). Inthis case, eight light source positions are simultaneously presentwithout fail, except that the light source position is on the X axis,the Y axis or the diagonal line (Y=X or Y=−X). Here, the values on thelight source coordinate are all normalized by the numerical aperture NAof a reduced size optical system of the exposure apparatus.

[0344]FIG. 38(c) shows the results of mapping the DOF of a mask pattern(width L=0.15 μm, opening width S=0 μm, see FIG. 38(a)) constituted by acomplete light-shielding film with respect to the position of each lightsource when exposure is performed using a circular light source having aradius of 0.05 from the positions of the light sources with coordinates(x, y) shown in FIG. 38(b). Here, the exposure is performed at anexposure intensity that allows the size of the line pattern (resistpattern) formed at the best focus is 0.12 μm, and the DOF is definedwith the largest focus width at which the pattern size is within0.12±0.012 μm with respect to focus variations during the exposure.Furthermore, a ArF light source is used as the exposure light source,and the numerical aperture of the reduced size optical system of theexposure apparatus is 0.6.

[0345] As shown in FIG. 38(c), the average of the DOFs corresponding tovarious light source positions is about 0.3 [m, and the DOF at patternexposure using a light source position with a distance from the originalpoint (X=0, Y=0) of 1 is about 0.3 μm. The light source positions inwhich the DOF is higher than the average are present locally, such asthe positions around a coordinate (X=0.5, Y=0.5), and positions obtainedby rotating this position by 90 degrees, 180 degrees, and 270 degreesaround the original point. Thus, better DOFs can be obtained by usingoblique incidence from these four light source positions. However, asseen from FIG. 38(c), in the case of the mask pattern constituted by acomplete light-shielding film, even if the DOF is improved by using, forexample, the above-described light source positions, the improvement isonly about twice the average of the DOF.

[0346] FIGS. 39(a) to (d) and FIGS. 40(a) to (d) are diagrams showingthe DOF maps corresponding to various light source positions in exposureusing a mask pattern constituted by a mask enhancer. More specifically,a mask enhancer having a mask pattern width of L (0.15 μm) and a widthof an opening serving as a phase shifter of S (0.04 μm, 0.08 μm, or 0.10μm) as shown in FIG. 39(a) is assumed as the mask pattern for DOF mapevaluation. Here, as described above, the DOF map is four rotationalsymmetric with respect to the original point on the light sourcecoordinate, so that in the following description, only a portioncorresponding to the first quadrant (region with X≧0 and Y≧0) on thelight source coordinate on the DOF map is shown.

[0347] FIGS. 39(b) to (d) are diagrams showing the results of mappingDOF of a mask pattern constituted by the mask enhancer shown in FIG.39(a) with respect to the position of each light source. FIG. 39(b)shows the results obtained when the opening width S is 0.04 μm, FIG.39(c) shows the results obtained when the opening width S is 0.08 μm,and FIG. 39(d) shows the results obtained when the opening width S is0.10 μm. Here, a ArF light source is used as the exposure light source,and the numerical aperture of the reduced size optical system of theexposure apparatus is 0.6. As shown in FIGS. 39(b) to (d), as theopening width S of the mask enhancer increases, the DOF increasessignificantly by off-axis exposure when the light source is present inthe vicinity of a coordinate (X=0.5, Y=0.5).

[0348]FIG. 40(a) is a diagram showing the results of plotting DOF valuescorresponding to the position of the light source on the X=Y line(diagonal line) in the DOF map shown in each of FIG. 38(c) and FIGS.39(b) to (d). As shown in FIG. 40(a), in the off-axis exposure from the45 degree directions, the DOF can be improved drastically as the openingwidth S of the mask enhancer increases, by performing off-axis exposurefrom the light source position with a distance from the original pointon the light source coordinate of 0.4 or more and 0.85 or less. On theother hand, in the off-axis exposure from the 45 degree directions, whenthe off-axis exposure from the light source position with a distancefrom the original point on the light source coordinate of 0.4 or less isperformed, the DOF are deteriorated as the opening width S of the maskenhancer increases.

[0349] FIGS. 40(b) to (d) show the regions in which the DOF is increasedor decreased by 0.05 μm or more from the DOF map (mask patternconstituted by a complete light-shielding film) shown in FIG. 38(c) inthe DOF map (mask pattern constituted by a mask enhancer) shown in eachof FIGS. 39(b) to (d). The results shown in FIGS. 40(b) to (d) indicatethat the DOF can be improved reliably by optically setting a reducedsize optical system of the exposure apparatus such that exposure can beperformed with the light source positions being present in the vicinityof a coordinate (X=0.5, Y=0.5) and a light source in a region with adistance from the original point on the light source coordinate of apredetermined value (about 0.4) or less being removed. In order toconfirm whether this is a general tendency or not, the inventor of thepresent invention obtained the DOF values corresponding to the positionof the light source on the diagonal line, as shown in FIG. 40(a), basedon each DOF map, by obtaining the DOF map of a mask pattern (L/S=0.15/0μm) constituted by a complete light-shielding film and the DOF map of amask pattern (L/S=0.15/0.02, 0.04, 0.06 μm) constituted by a maskenhancer, in each of the cases where a KrF light source and a F₂ lightsource are used with a numerical aperture of a reduction projectionoptical system of an exposure apparatus of 0.6 and where an ArF lightsource is used with a numerical aperture of a reduction projectionoptical system of an exposure apparatus of 0.7 and 0.8. FIGS. 41(a) to(d) show the results thereof. FIG. 41(a) show the DOF valuescorresponding to the position of the light source on the diagonal linewhen the numerical aperture of the reduction projection optical systemof the exposure apparatus is 0.6, and a KrF light source is used. FIG.41(b) show the DOF values corresponding to the position of the lightsource on the diagonal line when the numerical aperture of the reductionprojection optical system of the exposure apparatus is 0.6, and a F₂light source is used. FIG. 41(c) show the DOF values corresponding tothe position of the light source on the diagonal line when the numericalaperture of the reduction projection optical system of the exposureapparatus is 0.7, and a ArF light source is used. FIG. 41(d) show theDOF values corresponding to the position of the light source on thediagonal line when the numerical aperture of the reduction projectionoptical system of the exposure apparatus is 0.8, and a ArF light sourceis used. The results shown in FIGS. 41(a) to (d) indicate that thetendency that the DOF is improved by off-axis exposure in which thelight source positions are present in the vicinity of a coordinate(X=0.5, Y=0.5) is a general tendency.

[0350] In general, it is known that when off-axis exposure (off-axisillumination) is used to form a pattern arranged in a cycle of aboutλ/NA or less, the DOF characteristics are improved. However, whenoff-axis exposure is used to form an isolated pattern, the DOFcharacteristics are substantially not improved and the contrast of thelight intensity distribution is deteriorated, and therefore it issupposed to be not preferable to use off-axis exposure to form anisolated pattern. On the other hand, in the third embodiment, also whenforming an isolated pattern, the off-axis exposure is an optimalexposure method because of the effect of the DOF improvement and thecontrast improvement of the mask enhancer. Therefore, according to thethird embodiment, the optimal exposure method for forming an isolatedpattern is matched to that for forming a pattern arranged in a smallcycle, so that a fine pattern having an arbitrary layout can be formedwith high precision.

[0351] Fourth Embodiment

[0352] Hereinafter, a method for designing a mask pattern according to afourth embodiment of the present invention, more specifically, a methodfor designing a mask pattern for producing the photomask of the first orthe second embodiment, that is a photomask that improves the contrast ofthe light intensity distribution and the focus margin for exposure bycanceling the mask pattern diffracted light with the shifter transmittedlight having a phase opposite thereto will be described with referenceof the accompanying drawings.

[0353]FIG. 42 is a flowchart showing each process of the mask patterndesign method according to the fourth embodiment.

[0354] First, in a step S1, a layout (hereinafter, referred to as a“pattern layout”) of a mask pattern for forming a desired pattern(resist pattern) is produced, and the transmittance T of a phase shifterarranged in the mask pattern is set. FIG. 43(a) shows an example of apattern layout produced in the step S1.

[0355] Next, in a step S2, the pattern layout produced in the step S1 isdivided and an evaluation potion r is set in the vicinity of the centerof each pattern that has been divided (hereinafter, referred to as a“divided pattern”). FIG. 43(b) shows the manner in which the evaluationpoint r is set in each divided pattern in the step S2.

[0356] Next, in a step S3, mask data indicating that a light-shieldingpattern constituted by a light-shielding film is arranged in the entirepattern layout are created. This corresponds to a mask for evaluationfor calculating the light intensity of the mask pattern diffractedlight. FIG. 43(c) shows an example of the mask for evaluationcorresponding to the mask data produced in the step S3. The lightintensity Ic (r) projected and transferred on the position correspondingto each evaluation point r on the exposed material in exposure usingthis mask for evaluation is calculated by light intensity simulationsusing optical conditions of the exposure apparatus during actual use, orthe like.

[0357] Next, in a step S4, a divided pattern containing an evaluationpoint r for which Ic (r) calculated in the step S3 is larger than apredetermined It, that is, a divided pattern in which thelight-shielding properties are not sufficient in the evaluation point r,is extracted. FIG. 43(d) shows the divided pattern in which thelight-shielding properties are not sufficient in the evaluation point rextracted in the step S4. The divided pattern extracted in the step S4is a portion in which even if a light-shielding film is provided,sufficient light-shielding properties cannot be obtained because a largeamount of light is transmitted through the periphery of thelight-shielding film and goes into the back side of the light-shieldingfilm.

[0358] Next, in a step S5, mask data indicating that an opening isprovided in the divided pattern extracted in the step S4, and alight-shielding portion is provided in other portions in the photomaskare created. This corresponds to a mask for evaluation for calculatingthe maximum of the light intensity of the shifter transmitted light.FIG. 43(e) shows an example of the mask for evaluation corresponding tothe mask data produced in the step S5. The light intensity Io (r)projected and transferred on the position corresponding to eachevaluation point r on the exposed material in exposure using this maskfor evaluation is calculated by light intensity simulations usingoptical conditions of the exposure apparatus during actual use, or thelike. Thus, the maximum of the light intensity of the shiftertransmitted light in the case where a phase shifter is provided in thedivided pattern extracted in the step S4 can be estimated to be T×Io(r), so that it can be determined whether the light intensity (lightintensity Ic (r)) of the mask pattern diffracted light can be cancelled.

[0359] Next, in a step S6, using the value of the light intensity Io (r)and the value of the light intensity Ic (r) in each evaluation point r,the light intensity of each of the shifter transmitted light and themask pattern diffracted light is evaluated, so that the conditions toimprove the light-shielding properties are determined.

[0360] As described above, when the mask enhancer is used, a phaseshifter corresponding to an arbitrary transmittance from 0 to T can beformed by covering partially the phase shifter having a transmittance Twith a light-shielding film. However, when considering actual maskprocessing, the lower limit for the opening size is imposed, so that itis necessary to set the minimum size for the opening. Therefore, basedon this minimum, the smallest transmittance Tmin that can besubstantially generated is predetermined. In this case, in each dividedpattern, if Tmin×Io (r)≧4×Ic (r) is satisfied, the light-shieldingproperties becomes higher when no opening, that is, no phase shifter isprovided (see the first or the second embodiment), so that alight-shielding portion is provided in a divided pattern in which Ic(r)/Io (r) becomes smaller than Z4, where Z4=Tmin/4.

[0361] On the other hand, the width of the light-shielding film coveringthe phase shifter decreases as the opening is enlarged, so that there isa limitation regarding the size of the light-shielding portion that canbe formed on a photomask. In other words, light transmitted through thephase shifter provided in the light-shielding film has the upper limit,and based on this upper limit, the maximum transmittance Tmax (Tmax<T)that can be substantially generated is predetermined. In this case, ineach divided pattern, if Ic (r)≧Tmax×Io (r) is satisfied, thelight-shielding properties becomes higher when only phase shifter isprovided rather than providing the phase shifter partially covered bythe light-shielding film (that is, the mask enhancer), so that the phaseshifter is provided in the divided pattern in which Ic (r)/Io (r)becomes larger than Z1, where Z1=Tmax.

[0362] In other words, in each divided pattern, if Z4>Ic (r)/Io (r) issatisfied, the light-shielding portion is set, and if Z1≧Ic (r)/Io(r)≧Z4 is satisfied, the mask enhancer is set. If Ic (r)/Io (r)≧Z1 issatisfied, the phase shifter is set. However, when Tmin and Tmax are notpredetermined for simplification, Z1=T and Z4=T/4. FIG. 43(f) showsdivided patterns extracted in the step S4 in which the light-shieldingproperties are not sufficient and the phase shifter or the mask enhanceris set in the step S6.

[0363] Next, in the step S7, the size of the opening serving as a phaseshifter in the mask enhancer set in a divided pattern in the step S6 isdetermined. In this case, the condition in which the transmittance Tegenerated effectively by the mask enhancer maximizes the light-shieldingeffect is represented by Te=Ic (r)/Io (r). Furthermore, as described inthe second embodiment, the equivalent transmittance of the opening isrepresented by an approximate that is proportional to the opening arearatio (see FIG. 26(e)). Therefore, in order to make a phase shifterhaving a transmittance T substantially equal to a phase shifter having atransmittance Te, the area of the opening is reduced based on the rulerepresented by α×(Te/T)+β, where the coefficient such as α and β aredetermined depending on the optical parameter of the exposure apparatussuch as the wavelength of exposure light or the mask pattern size. Morespecifically, according to the above-described rule, an opening whoseopening area ratio is α×(Ic (r)/(Io(r)×T))+β is set so that the dividedpattern in which the mask enhancer is set effectively becomes the phaseshifter having a transmittance Te. In this case, if the area of thedivided pattern is Sc, and the area of the opening is So,

So=Sc×(α×(Ic (r)/(Io(r)×T))+β)

[0364] is satisfied. There is no particular limitation regarding theshape of the opening, as long as the opening area ratio is apredetermined value. However, simply, a shape obtained simply byreducing the pattern layout shape in accordance with the opening arearatio may be used. FIG. 43(g) shows that the opening having a shapeobtained by reducing the pattern layout shape in the step S7 is set inthe mask enhancer set in the divided pattern in the step S6.

[0365] Next, in a step S8, a pattern obtained by removing the phaseshifters (including the opening of the mask enhancer) that have been setup to the step S7 from the pattern layout is produced as alight-shielding portion pattern.

[0366] Finally, in a step S9, mask pattern data constituted by thelight-shielding portion pattern and the phase shifter pattern arecreated. FIG. 43(h) shows an example of the mask pattern data created inthe step S9. Thereafter, the mask pattern data are output and thus themask pattern design is ended. Thus, it is possible to create maskpattern data to realize the mask structure that can improve thelight-shielding effect by utilizing the shifter transmitted light havinga phase opposite to that of the mask pattern diffracted light in aregion where the light-shielding effect cannot be sufficiently obtainedwhen a light-shielding pattern is provided entirely in a desired patternlayout.

[0367] As described above, according to the fourth embodiment, thetransmittance of the phase shifter and the opening size of the maskenhancer that can maximize the light-shielding properties can beobtained based on the ratio in the light intensity between the maskpattern diffracted light and the shifter transmitted light, each ofwhich is calculated independently. Therefore, the transmittance of thephase shifter and the opening size of the mask enhancer that canmaximize the light-shielding properties can be obtained easily withrespect to an arbitrary layout of the mask pattern.

[0368] In the fourth embodiment, a shape obtained simply by reducing thepattern layout shape in accordance with the opening area ratio is usedas the shape of the opening set in the mask enhancer in the step S7, butthe shape of the opening can be any shape, as long as it has apredetermined opening area ratio, and is accommodated within the patternlayout. In other words, the opening shape can be changed, as long as theopening area ratio or the area of the openings provided in apredetermined range is not changed. However, in general, a shape thatdoes not cause any problem in actual mask processing is preferable. Forexample, an opening shape that forms a narrow light-shielding potionpattern, which causes peeling of the light-shielding film from thesubstrate, is not preferable. FIG. 44(a) shows 25 the results ofchanging the shape of the opening shown in FIG. 43(g) in such a mannerthat a chromium film serving as the light-shielding film on the mask ishardly peeled, that is, a narrow light-shielding portion pattern is notproduced. FIG. 44(b) shows mask pattern data corresponding to FIG.44(a).

[0369] Furthermore, in the fourth embodiment, the light-shielding filmor the light-shielding portion provided in the mask pattern layout(including divided patterns) may have a transmittance of 15% or lesswith respect to exposure light and generate a phase difference of(−30+360×n) degrees or more and (30+360×n) degrees or less, where n=aninteger, with respect to exposure light between the light-shielding filmor the light-shielding portion and the light-transmitting portion.

[0370] First Variation Example of the Fourth Embodiment

[0371] Hereinafter, a method for designing a mask pattern according to afirst variation example of the fourth embodiment of the presentinvention, more specifically, a method for designing a mask pattern forproducing the photomask of the first or the second embodiment will bedescribed with reference of the accompanying drawings.

[0372]FIGS. 45 and 46 are flowcharts showing each process of the maskpattern design method according to the first variation example of thefourth embodiment.

[0373] The first variation example of the fourth embodiment is differentfrom the fourth embodiment in a method for calculating the opening areaof the mask enhancer. More specifically, in the fourth embodiment, theopening area of the mask enhancer is obtained by approximatecalculations using only the opening area ratio, whereas in the firstvariation example of the fourth embodiment, the opening area of the maskenhancer is calculated more accurately.

[0374] As shown in FIGS. 45 and 46, the processing of the steps S1 to S6and the processing of the steps S8 and S9 in the first variation exampleof the fourth embodiment are totally the same as the processing of thesteps S1 to S6 and the processing of the steps S8 and S9 in the fourthembodiment shown in FIG. 42. That is, in the first variation example ofthe fourth embodiment, the processing of the step S7 in the fourthembodiment is replaced by the processing of the steps S10 to S14, morespecifically, the procedure of checking whether or not the opening ofthe mask enhancer can realize sufficient light-shielding effect andcorrecting the opening area based on the results. Thus, it is possibleto create the mask pattern data that can realize sufficientlight-shielding properties with the mask enhancer.

[0375] Hereinafter, the processing from the steps S10 to S14 will bedescribed with reference to FIGS. 45 and 46.

[0376] In the step S10, the opening area ratio is set using only theratio between the transmittance T of the phase shifter and the optimaltransmittance Te (=Ic (r)/Io (r)) that realize the maximumlight-shielding effect in the mask enhancer, and the size of the openingof the mask enhancer is determined based on the opening area ratio. Morespecifically, if the area of the divided pattern is Sc, and the area ofthe opening is So,

So=Sc×Ic (r)/(Io (r)×T)

[0377] is satisfied. Hereinafter, description below is based on theassumption that FIG. 43(a) shows the opening set at the step S10.

[0378] Next, in the step S11, mask data indicating that the opening isdisposed in portions in which the phase shifters (including the openingin the mask hanker) have been set up to the step S10, and alight-shielding portion is disposed in other portions in the photomaskis created. This corresponds to a mask for evaluation for calculatingthe light intensity of the shifter transmitted light accurately. FIG. 47shows an example of a mask for evaluation corresponding to the mask datacreated at the step S11. In exposure using this mask for evaluation, thelight intensity Io (r) projected and transferred on the positioncorresponding to each evaluation point r on an exposed material isrecalculated, for example with simulations of light intensity using theoptical conditions of the exposure apparatus for actual use. Thus, thelight intensity of the shifter transmitted light can be estimatedaccurately with T×Io (r), so that it can be determined accuratelywhether the light intensity (light intensity Ic (r)) of the mask patterndiffracted light can be cancelled sufficiently.

[0379] Next, in the step S12, it is checked whether or not therecalculated Io (r) in the step S11 is an appropriate intensity so as torealize the maximum light-shielding effect. Here, in a portion in whichthe size of the opening of the mask enhancer realizes an appropriateintensity so as to realize the maximum light-shielding effect, that sizeis determined for the opening of the mask enhancer. On the other hand,in a portion in which the above is not the case, the opening area ratiois set using only the ratio between the transmittance T of the phaseshifter and the optimal transmittance Te (=Ic (r)/Io (r)) that realizethe maximum light-shielding effect in the mask enhancer at this point,and the size of the opening of the mask enhancer is determined based onthe opening area ratio. More specifically, if the area of the openingobtained in the step S10 is So, the area So′ that is defined by:

So×Ic (r)/(Io (r)×T)

[0380] is obtained as a new area of the opening. Here, it can bedetermined whether or not the size of the opening of the mask enhancerhas realized the maximum light-shielding effect, by determining whetheror not the mask pattern diffracted light is sufficiently cancelled bythe shifter transmitted light, that is, whether or not T×Io (r)≈Ic (r)is satisfied. Therefore, according to So′=So×Ic (r)/(Io (r)×T), when theshifter transmitted light is excessive, a correction of making theopening small is added, and when the shifter transmitted light is toolittle, a correction of enlarging the opening is added.

[0381] Next, in the step S13, it is determined whether or not theopening area is corrected in the step S12, and when the opening area iscorrected, in a step S14, the opening area So is updated by the openingare So′, and then the procedure goes back to the step S11. In otherwords, based on the content of the correction of the opening area, maskdata corresponding to a mask for evaluation for calculating the lightintensity of the shifter transmitted light accurately is created againand the process of recalculating the light intensity Io (r) is repeateduntil the Ic (r) is cancelled sufficiently by Io (r). On the other hand,when the opening area is not updated, the procedure goes to a step S8and the following steps.

[0382] According to the first variation example of the fourthembodiment, in addition to the effect of the fourth embodiment, thefollowing effect can be obtained. Since it is checked whether or not theopening of the mask enhancer can realize sufficient light-shieldingeffect and the opening area is corrected based the results thereof, maskpattern data that can realize sufficient light-shielding properties bythe mask enhancer can be created reliably.

[0383] Furthermore, in the first variation example of the fourthembodiment, the light-shielding film or the light-shielding portionprovided in the mask pattern layout (including divided patterns) mayhave a transmittance of 15% or less with respect to exposure light andgenerate a phase difference of (−30+360×n) degrees or more and(30+360×n) degrees or less, where n=an integer, with respect to exposurelight between the light-shielding film or the light-shielding portionand the light-transmitting portion.

[0384] Second Variation Example of the Fourth Embodiment

[0385] Hereinafter, a method for designing a mask pattern according to asecond variation example of the fourth embodiment of the presentinvention, more specifically, a method for designing a mask pattern forproducing the photomask of the first or the second embodiment will bedescribed with reference of the accompanying drawings.

[0386]FIG. 48 is a flowchart showing each process of the mask patterndesign method according to the second variation example of the fourthembodiment.

[0387] The second variation example of the fourth embodiment isdifferent from the fourth embodiment in the following aspects. In thefourth embodiment, the phase shifter, the mask enhancer and thelight-shielding portion are used as the mask pattern, whereas in thesecond variation example of the fourth embodiment, only the phaseshifter and the light-shielding portion are used as the mask patternwithout using the mask enhancer.

[0388] As shown in FIG. 48, the processing of the steps S1 to S5 and theprocessing of the step S9 in the second variation example of the fourthembodiment are totally the same as the processing of the steps S1 to S5and the processing of the step S9 in the fourth embodiment shown in FIG.42. That is, in the second variation example of the fourth embodiment,the processing of the steps S6 to S8 in the fourth embodiment isreplaced by the processing of the step S20. More specifically, in thestep S6 in the fourth embodiment, the range of the transmittance Tegenerated effectively by the mask enhancer is set from Tmin to Tmax thatis represented by 0<Tmin≦Tmax<T, whereas in the second variation exampleof the fourth embodiment, a situation satisfying Tmin=Tmax=T is assumed.

[0389] In the step S20, each of the light intensity of shiftertransmitted light and the mask pattern diffracted light is evaluatedusing the value of the light intensity Io(r) and the value of the lightintensity Ic(r) at each evaluation point r, so that a condition forimproving the light-shielding properties is determined. In this case, ineach divided pattern, if T/4>Ic (r)/Io (r) is satisfied, thelight-shielding portion is set, and if Ic (r)/Io (r)≧T/4 is satisfied,the phase shifter is set. Thus, the light-shielding properties of eachdivided pattern can be improved, based on a simple determination whichcase can provide higher light-shielding properties for each dividedpattern, when the phase shifter is used or when the light-shieldingportion is used. FIG. 49(a) shows the phase shifter set in the step S20with respect to a divided pattern extracted in the step S4 in which thelight-shielding properties are not sufficient.

[0390] In the second variation example of the fourth embodiment, thestep of providing the opening of the mask enhancer (processing of thestep S7 in the fourth embodiment) and the step of producing alight-shielding portion pattern by removing the phase shifter includingthe opening of the mask enhancer from the pattern layout (processing ofthe step S8 in the fourth embodiment) are not necessary.

[0391]FIG. 49(b) shows an example of mask pattern data created in thesecond variation example of the fourth embodiment.

[0392] According to the second variation example of the fourthembodiment, in addition to the advantages of the fourth embodiment, thefollowing advantages can be obtained. Only the phase shifter and thelight-shielding portion are used without using the mask enhancer as themask pattern, mask pattern data that can realize sufficientlight-shielding properties can be created in a simple manner.

[0393] Furthermore, in the second variation example of the fourthembodiment, the light-shielding film or the light-shielding portionprovided in the mask pattern layout (including divided patterns) mayhave a transmittance of 15% or less with respect to exposure light andgenerate a phase difference of (−30+360×n) degrees or more and(30+360×n) degrees or less, where n=an integer, with respect to exposurelight between the light-shielding film or the light-shielding portionand the light-transmitting portion.

[0394] Third Variation Example of the Fourth Embodiment

[0395] Hereinafter, a method for designing a mask pattern according to athird variation example of the fourth embodiment of the presentinvention, more specifically, a method for designing a mask pattern forproducing the photomask of the first or the second embodiment will bedescribed with reference of the accompanying drawings.

[0396]FIG. 50 is a flowchart showing each process of a mask patterndesign method according to a third variation example of the fourthembodiment.

[0397] The third variation example of the fourth embodiment is differentfrom the fourth embodiment in the following aspects. In the fourthembodiment, the mask pattern is designed so as to improve thelight-shielding properties based on the results of optical simulationsusing mask data. On the other hand, in the third variation example ofthe fourth embodiment, although the determination of a condition underwhich a phase shifter having a transmittance T can realizelight-shielding properties higher than those of a light-shielding filmis not perfect, a mask pattern that can improve the light-shieldingproperties is designed, based on the pattern layout width.

[0398] More specifically, first, in a step S1, as in the fourthembodiment, a pattern layout of a mask pattern for forming a desiredpattern (resist pattern) is created and the transmittance T of a phaseshifter provided in the mask pattern is determined.

[0399] Next, in a step S30, the light intensity Ih (T, L) projected andtransferred on the position corresponding to the center of the maskpattern on an exposed material in exposure using a mask patternconstituted by a phase shifter having a transmittance T and a width L iscalculated with, for example, optical simulations using an opticalcondition of the exposure for actual use. Furthermore, the lightintensity Ic (L) projected and transferred on the position correspondingto the center of the mask pattern on an exposed material in exposureusing a mask pattern constituted by a light-shielding film having awidth L is calculated in the same manner. The minimum width L at whichthe light intensity Ih (T, L) is smaller than the light intensity Ic(L), in other words, the maximum width L at which the light-shieldingeffect of the phase shifter is higher than that of the light-shieldingfilm, is obtained as the critical width Ls.

[0400] Next, in a step S31, a partial pattern whose width is thecritical width Ls or less is extracted from the pattern layout.

[0401] Next, in a step S32, a phase shifter is provided in the partialpattern extracted in the step S31 and a light-shielding portion isprovided in other portions than that.

[0402] Finally, in a step S9, as in the fourth embodiment, mask patterndata constituted by the light-shielding portion pattern and the phaseshifter pattern are created. Thereafter, the mask pattern data areoutput and thus the mask pattern design is ended.

[0403] According to the third variation example of the fourthembodiment, the mask pattern design that can improve the light-shieldingproperties is performed, based on the pattern layout width, withoutusing optical simulations using the mask data, so that the mask patterndesign can be simple.

[0404] In the third variation example of the fourth embodiment, thelight-shielding film or the light-shielding portion provided in the maskpattern layout (including divided patterns) may have a transmittance of15% or less with respect to exposure light and generate a phasedifference of (−30+360×n) degrees or more and (30+360×n) degrees orless, where n=an integer, with respect to exposure light between thelight-shielding film or the light-shielding portion and thelight-transmitting portion.

[0405] Fourth Variation Example of the Fourth Embodiment

[0406] Hereinafter, a method for designing a mask pattern according to afourth variation example of the fourth embodiment of the presentinvention, more specifically, a method for designing a mask pattern forproducing the photomask of the first or the second embodiment will bedescribed with reference of the accompanying drawings.

[0407]FIG. 51 is a flowchart showing each process of a mask patterndesign method according to a fourth variation example of the fourthembodiment.

[0408] The fourth variation example of the fourth embodiment isdifferent from the fourth embodiment in the following aspects. In thefourth embodiment, one kind of transmittance T is used as thetransmittance of the phase shifter, but in the fourth variation exampleof the fourth embodiment, two kinds of transmittances T1 and T2 (whereT1>T2) are used as the transmittance of the phase shifter. Furthermore,in the fourth embodiment, the phase shifter, the mask enhancer and thelight-shielding portion are used as the mask pattern, whereas in thefourth variation example of the fourth embodiment, only the phaseshifter and the light-shielding portion are used as the mask patternwithout using the mask enhancer, as in the second variation example ofthe fourth embodiment.

[0409] As shown in FIG. 51, the processing of the steps S2 to S5 and theprocessing of the step S9 in the fourth variation example of the fourthembodiment are totally the same as the processing of the steps S2 to S5and the processing of the step S9 in the fourth embodiment shown in FIG.42. That is, in the fourth variation example of the fourth embodiment,the processing of the step SI in the fourth embodiment is replaced bythe processing of the step S40, and the processing of the steps S6 to S8in the fourth embodiment is replaced by the processing of the steps S41and S42.

[0410] In other words, in a step S40, a pattern layout of a mask patternfor forming a desired pattern (resist pattern) is created and the twotransmittances T1 and T2 (where T1>T2) of the phase shifter provided inthe mask pattern are determined.

[0411] Furthermore, each processing of the steps S2 to S5 is performed,and then in a step S41, each of the light intensity of shiftertransmitted light and the mask pattern diffracted light is evaluatedusing the value of the light intensity lo (r) and the value of the lightintensity Ic (r) at each evaluation point r, so that a condition forimproving the light-shielding properties is determined. In this case, ineach divided pattern, if T2/4>Ic (r)/Io (r) is satisfied, thelight-shielding portion is set, and if Ic (r)/Io (r)≧T2/4 is satisfied,the phase shifter is set. In other words, a portion in which thelight-shielding properties can be improved to be better than those ofthe light-shielding film by using a phase shifter having the lowesttransmittance of the usable phase shifters is first extracted based onthat phase shifter. This is because a portion in which thelight-shielding properties can be improved to be better than those ofthe light-shielding film by using phase shifter having a hightransmittance is limited to a portion inside the portion in which thelight-shielding properties can be improved better than those of thelight-shielding film by using phase shifter having a transmittance lowerthan that. The processing of the step S41 is the same as the processingthe step 20 in the second variation example of the fourth embodimentshown in FIG. 48, except that the single transmittance T is replaced bythe minimum value (T2) of the transmittances that can be used.

[0412] Next, in a step S42, in each divided pattern in which phaseshifters are set, it is determined which phase shifter has anappropriate transmittance for use. In this case, as described in thefirst embodiment, in a mask pattern portion in which

Ic/Io>(T1 ^(0.5)+T2 ^(0.5))×(T1 ^(0.5)+T2 ^(0.5))/2

[0413] is satisfied, the phase shifter having a transmittance T1 can beselected, and in a mask pattern portion in which

Ic/Io≦(T1 ^(0.5)+T2 ^(0.5))×(T1 ^(0.5)+T2 ^(0.5))/2

[0414] is satisfied, the phase shifter having a transmittance T2 can beselected. FIG. 52(a) shows the phase shifters having two kinds oftransmittances T1 and T2 set in the steps S41 and S42 with respect to adivided pattern extracted in the step S4 in which the light-shieldingproperties are not sufficient.

[0415] In the fourth variation example of the fourth embodiment, thestep of providing the opening of the mask enhancer (processing of thestep S7 in the fourth embodiment) and the step of producing alight-shielding portion pattern by removing the phase shifter includingthe opening of the mask enhancer from the pattern layout (processing ofthe step S8 in the fourth embodiment) are not necessary.

[0416]FIG. 52(b) shows an example of mask pattern data created in thefourth variation example of the fourth embodiment.

[0417] According to the fourth variation example of the fourthembodiment, in addition to the advantages of the fourth embodiment, thefollowing advantages can be obtained. Only the phase shifter and thelight-shielding portion are used without using the mask enhancer as themask pattern, mask pattern data that can realize sufficientlight-shielding properties can be created in a simple manner.Furthermore, in a situation where phase shifters having a plurality oftransmittances can be used, the phase shifters having differenttransmittances can be set so that higher light-shielding properties canbe realized, so that phase shifters having different transmittances canbe disposed at appropriated positions.

[0418] Furthermore, in the fourth variation example of the fourthembodiment, three or more kinds of transmittances for the phase shifterscan be used.

[0419] Furthermore, in the fourth variation example of the fourthembodiment, the light-shielding film or the light-shielding portionprovided in the mask pattern layout (including divided patterns) mayhave a transmittance of 15% or less with respect to exposure light andgenerate a phase difference of (−30+360×n) degrees or more and(30+360×n) degrees or less, where n=an integer, with respect to exposurelight between the light-shielding film or the light-shielding portionand the light-transmitting portion.

1. A photomask comprising a mask pattern having light-shieldingproperties with respect to exposure light provided on a transparentsubstrate having light-transmitting properties with respect to theexposure light, wherein the mask pattern includes a phase shifter thatgenerates a phase difference of (150+360×n) degrees or more and(210+360×n) degrees or less, where n=an integer, with respect to theexposure light between the phase shifter and a light-transmittingportion in which the mask pattern is not formed on the transparentsubstrate, and a first light intensity generated in a light-shieldedimage formation region corresponding to the mask pattern on an exposedmaterial by the exposure light transmitted through the phase shifter isnot more than four times a second light intensity generated in thelight-shielded image formation region by the exposure light that istransmitted through a periphery of the mask pattern on the transparentsubstrate and goes into a back side of the mask pattern.
 2. Thephotomask according to claim 1, wherein the phase shifter is obtained byforming a transparent film having a transmittance different from that ofthe transparent substrate with respect to the exposure light on thetransparent substrate.
 3. The photomask according to claim 1, whereinthe phase shifter is obtained by etching the transparent substrate. 4.The photomask according to claim 1, wherein the mask pattern has alight-shielding film having a same outer shape, and the phase shifter isdisposed in an opening provided in the light-shielding film.
 5. Thephotomask according to claim 4, wherein the light-shielding film havingthe same outer shape has a transmittance of 15% or less with respect tothe exposure light and generates a phase difference of (−30+360×n)degrees or more and (30+360×n) degrees or less, where n=an integer, withrespect to the exposure light between the light-shielding film and thelight-transmitting portion.
 6. A photomask comprising a mask patternhaving light-shielding properties with respect to exposure lightprovided on a transparent substrate having light-transmitting propertieswith respect to the exposure light, wherein the mask pattern includes aphase shifter that generates a phase difference of (150+360×n) degreesor more and (210+360×n) degrees or less, where n=an integer, withrespect to the exposure light between the phase shifter and alight-transmitting portion in which the mask pattern is not formed onthe transparent substrate, and a first light intensity generated in alight-shielded image formation region corresponding to the mask patternon an exposed material by the exposure light transmitted through thephase shifter is between 0.5 times and 2 times a second light intensitygenerated in the light-shielded image formation region by the exposurelight that is transmitted through a periphery of the mask pattern on thetransparent substrate and goes into a back side of the mask pattern. 7.The photomask according to claim 6, wherein the phase shifter isobtained by forming a transparent film having a transmittance differentfrom that of the transparent substrate with respect to the exposurelight on the transparent substrate.
 8. The photomask according to claim6, wherein the phase shifter is obtained by etching the transparentsubstrate.
 9. The photomask according to claim 6, wherein the maskpattern has a light-shielding film having a same outer shape, and thephase shifter is disposed in an opening provided in the light-shieldingfilm.
 10. The photomask according to claim 9, wherein thelight-shielding film having the same outer shape has a transmittance of15% or less with respect to the exposure light and generates a phasedifference of (−30+360×n) degrees or more and (30+360×n) degrees orless, where n=an integer, with respect to the exposure light between thelight-shielding film and the light-transmitting portion.
 11. A methodfor forming a pattern using the photomask according to claim 1,comprising: forming a positive resist film on a substrate, irradiatingthe resist film with the exposure light through the photomask, andforming a resist pattern by developing the resist film irradiated withthe exposure light so as to remove portions other than the portioncorresponding to the mask pattern in the resist film, wherein when awidth of the portion corresponding to the mask pattern in the resistfilm is L, L≦0.4×λ/NA is satisfied, where λ is a wavelength of theexposure light, and NA is a numerical aperture of a reduction projectionoptical system of an exposure apparatus.
 12. The method for forming apattern according to claim 11, wherein the step of irradiating with theexposure light is performed using an off-axis illumination method. 13.The method for forming a pattern according to claim 12, wherein adirection in which the exposure light is incident to the photomask isset such that an intensity of the exposure light with which the resistfilm is irradiated has a minimum value in the portion corresponding tothe mask pattern in the resist film.
 14. The method for forming apattern according to claim 12, wherein a direction in which the exposurelight is incident to the photomask is set such that an intensity of theexposure light with which the resist film is irradiated has a minimumvalue in the portion corresponding to the mask pattern in the resistfilm and the minimum value is smaller at a defocus position than at abest focus position.
 15. A method for forming a pattern using thephotomask according to claim 1, comprising: forming a negative resistfilm on a substrate, irradiating the resist film with the exposure lightthrough the photomask, and forming a resist pattern by developing theresist film irradiated with the exposure light so as to remove theportion corresponding to the mask pattern in the resist film, whereinwhen a width of the portion corresponding to the mask pattern in theresist film is L, L≦0.4×λ/NA is satisfied, where λ is a wavelength ofthe exposure light, and NA is a numerical aperture of a reductionprojection optical system of an exposure apparatus.
 16. The method forforming a pattern according to claim 15, wherein the step of irradiatingwith the exposure light is performed using an off-axis illuminationmethod.
 17. The method for forming a pattern according to claim 16,wherein a direction in which the exposure light is incident to thephotomask is set such that an intensity of the exposure light with whichthe resist film is irradiated has a minimum value in the portioncorresponding to the mask pattern in the resist film.
 18. The method forforming a pattern according to claim 16, wherein a direction in whichthe exposure light is incident to the photomask is set such that anintensity of the exposure light with which the resist film is irradiatedhas a minimum value in the portion corresponding to the mask pattern inthe resist film and the minimum value is smaller at a defocus positionthan at a best focus position.
 19. A method for forming a pattern usingthe photomask according to claim 2, comprising: forming a positiveresist film on a substrate, irradiating the resist film with theexposure light through the photomask, and forming a resist pattern bydeveloping the resist film irradiated with the exposure light so as toremove portions other than the portion corresponding to the mask patternin the resist film, wherein when a width of the portion corresponding tothe mask pattern in the resist film is L, L≦0.4×λ/NA is satisfied, whereλ is a wavelength of the exposure light, and NA is a numerical apertureof a reduction projection optical system of an exposure apparatus. 20.The method for forming a pattern according to claim 19, wherein the stepof irradiating with the exposure light is performed using an off-axisillumination method.
 21. The method for forming a pattern according toclaim 20, wherein a direction in which the exposure light is incident tothe photomask is set such that an intensity of the exposure light withwhich the resist film is irradiated has a minimum value in the portioncorresponding to the mask pattern in the resist film.
 22. The method forforming a pattern according to claim 20, wherein a direction in whichthe exposure light is incident to the photomask is set such that anintensity of the exposure light with which the resist film is irradiatedhas a minimum value in the portion corresponding to the mask pattern inthe resist film and the minimum value is smaller at a defocus positionthan at a best focus position.
 23. A method for forming a pattern usingthe photomask according to claim 2, comprising: forming a negativeresist film on a substrate, irradiating the resist film with theexposure light through the photomask, and forming a resist pattern bydeveloping the resist film irradiated with the exposure light so as toremove the portion corresponding to the mask pattern in the resist film,wherein when a width of the portion corresponding to the mask pattern inthe resist film is L, L≦0.4×λ/NA is satisfied, where λ is a wavelengthof the exposure light, and NA is a numerical aperture of a reductionprojection optical system of an exposure apparatus.
 24. The method forforming a pattern according to claim 23, wherein the step of irradiatingwith the exposure light is performed using an off-axis illuminationmethod.
 25. The method for forming a pattern according to claim 24,wherein a direction in which the exposure light is incident to thephotomask is set such that an intensity of the exposure light with whichthe resist film is irradiated has a minimum value in the portioncorresponding to the mask pattern in the resist film.
 26. The method forforming a pattern according to claim 24, wherein a direction in whichthe exposure light is incident to the photomask is set such that anintensity of the exposure light with which the resist film is irradiatedhas a minimum value in the portion corresponding to the mask pattern inthe resist film and the minimum value is smaller at a defocus positionthan at a best focus position.
 27. A method for producing a photomaskcomprising a mask pattern having light-shielding properties with respectto exposure light provided on a transparent substrate havinglight-transmitting properties with respect to the exposure light, themethod comprising: forming a phase shifter that generates a phasedifference of (150+360×n) degrees or more and (210+360×n) degrees orless, where n=an integer, with respect to the exposure light between thephase shifter and a light-transmitting portion in which the mask patternis not formed on the transparent substrate in a region serving as themask pattern, wherein the step of forming a phase shifter comprisesforming a phase shifter such that a first light intensity generated in alight-shielded image formation region corresponding to the mask patternon an exposed material by the exposure light transmitted through thephase shifter is proportional to a second light intensity generated inthe light-shielded image formation region by the exposure light that istransmitted through a periphery of the mask pattern on the transparentsubstrate and goes into a back side of the mask pattern.
 28. The methodfor producing a photomask according to claim 27, wherein the phaseshifter has a transmittance different from that of the transparentsubstrate with respect to the exposure light, and the step of formingthe phase shifter includes determining a formation position and thetransmittance of the phase shifter such that the first light intensityis not more than four times the second light intensity.
 29. The methodfor producing a photomask according to claim 27, wherein the phaseshifter has a transmittance different from that of the transparentsubstrate with respect to the exposure light, and the step of formingthe phase shifter includes determining a formation position and thetransmittance of the phase shifter such that the first light intensityis between 0.5 times and 2 times the second light intensity.
 30. Themethod for producing a photomask according to claim 27, wherein the maskpattern has a light-shielding film having a same outer shape, the phaseshifter is disposed in an opening provided in the light-shielding film,and the step of forming the phase shifter includes determining a widthof the opening such that the first light intensity is equal to apredetermined value.
 31. The method for producing a photomask accordingto claim 30, wherein when a width of the mask pattern is Lm,Lm≦(0.5×λ/NA)×M is satisfied, where λ is a wavelength of the exposurelight, NA is a numerical aperture of a reduction projection opticalsystem of an exposure apparatus, and M is a magnification factor of thereduction projection optical system.
 32. The method for producing aphotomask according to claim 27, wherein the mask pattern has alight-shielding film having a same outer shape, the phase shifter isdisposed in an opening provided in the light-shielding film, and thestep of forming the phase shifter includes determining a width of theopening such that the first light intensity is not more than four timesthe second light intensity.
 33. The method for producing a photomaskaccording to claim 32, wherein when a width of the mask pattern is Lm,Lm≦(0.5×λ/NA)×M is satisfied,. where λ is a wavelength of the exposurelight, NA is a numerical aperture of a reduction projection opticalsystem of an exposure apparatus, and M is a magnification factor of thereduction projection optical system.
 34. The method for producing aphotomask according to claim 27, wherein the mask pattern has alight-shielding film having a same outer shape, the phase shifter isdisposed in an opening provided in the light-shielding film, and thestep of forming the phase shifter includes determining a width of theopening such that the first light intensity is between 0.5 times and 2times the second light intensity.
 35. The method for producing aphotomask according to claim 34, wherein when a width of the maskpattern is Lm, Lm≦(0.5×λ/NA)×M is satisfied, where λ is a wavelength ofthe exposure light, NA is a numerical aperture of a reduction projectionoptical system of an exposure apparatus, and M is a magnification factorof the reduction projection optical system.
 36. A method for producing aphotomask comprising a mask pattern having light-shielding propertieswith respect to exposure light provided on a transparent substratehaving light-transmitting properties with respect to the exposure light,the method comprising: forming a phase shifter that generates a phasedifference of (150+360×n) degrees or more and (210+360×n) degrees orless, where n=an integer, with respect to the exposure light between thephase shifter and a light-transmitting portion in which the mask patternis not formed on the transparent substrate in a region serving as themask pattern, wherein the step of forming the phase shifter includesforming the phase shifter such that a first light intensity generated ina light-shielded image formation region corresponding to the maskpattern on an exposed material by the exposure light transmitted throughthe photomask when a periphery of the mask pattern on the transparentsubstrate is covered with a light-shielding film is proportional to asecond light intensity generated in the light-shielded image formationregion by the exposure light transmitted through the photomask when themask pattern is constituted only by a light-shielding film.
 37. Themethod for producing a photomask according to claim 36, wherein thelight-shielding film constituting the mask pattern has a transmittanceof 15% or less with respect to the exposure light and generates a phasedifference of (−30+360×n) degrees or more and (30+360×n) degrees orless, where n=an integer, with respect to the exposure light between thelight-shielding film and the light-transmitting portion.
 38. The methodfor producing a photomask according to claim 36, wherein the phaseshifter has a transmittance different from that of the transparentsubstrate with respect to the exposure light, and the step of formingthe phase shifter includes determining a formation position and thetransmittance of the phase shifter such that the first light intensityis not more than four times the second light intensity.
 39. The methodfor producing a photomask according to claim 36, wherein the phaseshifter has a transmittance different from that of the transparentsubstrate with respect to the exposure light, and the step of formingthe phase shifter includes determining a formation position and thetransmittance of the phase shifter such that the first light intensityis between 0.5 times and 2 times the second light intensity.
 40. Themethod for producing a photomask according to claim 36, wherein the maskpattern has a light-shielding film having a same outer shape, the phaseshifter is disposed in an opening provided in the light-shielding film,and the step of forming the phase shifter includes determining a widthof the opening such that the first light intensity is equal to apredetermined value.
 41. The method for producing a photomask accordingto claim 40, wherein when a width of the mask pattern is Lm,Lm≦(0.5×λ/NA)×M is satisfied, where λ is a wavelength of the exposurelight, NA is a numerical aperture of a reduction projection opticalsystem of an exposure apparatus, and M is a magnification factor of thereduction projection optical system.
 42. The method for producing aphotomask according to claim 36, wherein the mask pattern has alight-shielding film having a same outer shape, the phase shifter isdisposed in an opening provided in the light-shielding film, and thestep of forming the phase shifter includes determining a width of theopening such that the first light intensity is not more than four timesthe second light intensity.
 43. The method for producing a photomaskaccording to claim 42, wherein when a width of the mask pattern is Lm,Lm≦(0.5×λ/NA)×M is satisfied, where λ is a wavelength of the exposurelight, NA is a numerical aperture of a reduction projection opticalsystem of an exposure apparatus, and M is a magnification factor of thereduction projection optical system.
 44. The method for producing aphotomask according to claim 36, wherein the mask pattern has alight-shielding film having a same outer shape, the phase shifter isdisposed in an opening provided in the light-shielding film, and thestep of forming the phase shifter includes determining a width of theopening such that the first light intensity is between 0.5 times and 2times the second light intensity.
 45. The method for producing aphotomask according to claim 44, wherein when a width of the maskpattern is Lm, Lm≦(0.5×λ/NA)×M is satisfied, where λ is a wavelength ofthe exposure light, NA is a numerical aperture of a reduction projectionoptical system of an exposure apparatus, and M is a magnification factorof the reduction projection optical system.
 46. A method for producing aphotomask comprising a mask pattern having light-shielding propertieswith respect to exposure light provided on a transparent substratehaving light-transmitting properties with respect to the exposure light,the method comprising: forming a phase shifter that generates a phasedifference of (150+360×n) degrees or more and (210+360×n) degrees orless, where n=an integer, with respect to the exposure light between thephase shifter and a light-transmitting portion in which the mask patternis not formed on the transparent substrate and has a transmittance T(where 0<T<1) with respect to the exposure light, the phase shifterbeing formed in a region serving as the mask pattern, wherein the stepof forming the phase shifter includes: calculating a light intensity Iagenerated in a light-shielded image formation region corresponding tothe mask pattern on an exposed material by the exposure lighttransmitted through the photomask when the mask pattern is constitutedonly by a light-shielding film, calculating a light intensity Ibgenerated in the light-shielded image formation region by the exposurelight transmitted through the photomask when the transmittance T is 1,and a periphery of the mask pattern on the transparent substrate iscovered with a light-shielding film, and determining a formationposition and the transmittance T of the phase shifter such that4×Ia≧T×Ib is satisfied.
 47. The method for producing a photomaskaccording to claim 46, wherein the light-shielding film constituting themask pattern has a transmittance of 15% or less with respect to theexposure light and generates a phase difference of (−30+360×n) degreesor more and (30+360×n) degrees or less, where n=an integer, with respectto the exposure light between the light-shielding film and thelight-transmitting portion.
 48. A method for producing a photomaskcomprising a mask pattern having light-shielding properties with respectto exposure light provided on a transparent substrate havinglight-transmitting properties with respect to the exposure light, themethod comprising: forming a phase shifter that generates a phasedifference of (150+360×n) degrees or more and (210+360×n) degrees orless, where n=an integer, with respect to the exposure light between thephase shifter and the light-transmitting portion in which the maskpattern is not formed on the transparent substrate and has atransmittance T (where 0<T<1) with respect to the exposure light, thephase shifter being formed in a region serving as the mask pattern,wherein the step of forming the phase shifter includes: calculating alight intensity Ia generated in a light-shielded image formation regioncorresponding to the mask pattern on an exposed material by the exposurelight transmitted through the photomask when the mask pattern isconstituted only by a light-shielding film, calculating a lightintensity Ib generated in the light-shielded image formation region bythe exposure light transmitted through the photomask when thetransmittance T is 1, and a periphery of the mask pattern on thetransparent substrate is covered with a light-shielding film, anddetermining a formation position and the transmittance T of the phaseshifter such that 2×Ia≧T×Ib≧0.5×Ia is satisfied.
 49. The method forproducing a photomask according to claim 48, wherein the light-shieldingfilm constituting the mask pattern has a transmittance of 15% or lesswith respect to the exposure light and generates a phase difference of(−30+360×n) degrees or more and (30+360×n) degrees or less, where n=aninteger, with respect to the exposure light between the light-shieldingfilm and the light-transmitting portion.
 50. A method for designing amask pattern for forming a photomask comprising a mask pattern havinglight-shielding properties with respect to exposure light provided on atransparent substrate having light-transmitting properties with respectto the exposure light, wherein the mask pattern has a phase shifter thatgenerates a phase difference of (150+360×n) degrees or more and(210+360×n) degrees or less, where n=an integer, with respect to theexposure light between the phase shifter and a light-transmittingportion in which the mask pattern is not formed on the transparentsubstrate, the method comprising: creating a pattern layout that is alayout of the mask pattern and determining a transmittance T of thephase shifter, generating a plurality of divided patterns by dividingthe pattern layout, calculating a light intensity Ic generated in alight-shielded image formation region corresponding to each of thedivided patterns on an exposed material by the exposure lighttransmitted through the photomask when a light-shielding film isdisposed in the entire pattern layout, calculating a light intensity logenerated in the light-shielded image formation region by the exposurelight transmitted through the photomask when an opening is provided in adivided pattern in which the corresponding light intensity Ic is lagerthan a predetermined value of the divided patterns, and alight-shielding film is provided entirely in a portion other than thatportion in the photomask, and providing the phase shifter in a dividedpattern in which Ic/Io>T is satisfied of the divided patterns, providinga light-shielding portion in a divided pattern in which T/4>Ic/Io issatisfied of the divided patterns, and providing a light-shieldingportion having an opening serving as the phase shifter in a dividedpattern in which T≧Ic/Io≧T/4 is satisfied of the divided patterns. 51.The method for designing a mask pattern according to claim 50, whereinthe light-shielding film or the light-shielding portion provided in thepattern layout has a transmittance of 15% or less with respect to theexposure light and generates a phase difference of (−30+360×n) degreesor more and (30+360×n) degrees or less, where n=an integer, with respectto the exposure light between the light-shielding film or thelight-shielding portion and the light-transmitting portion.
 52. A methodfor designing a mask pattern for forming a photomask comprising a maskpattern having light-shielding properties with respect to exposure lightprovided on a transparent substrate having light-transmitting propertieswith respect to the exposure light, wherein the mask pattern has a phaseshifter that generates a phase difference of (150+360×n) degrees or moreand (210+360×n) degrees or less, where n=an integer, with respect to theexposure light between the phase shifter and a light-transmittingportion in which the mask pattern is not formed on the transparentsubstrate, the method comprising: creating a pattern layout that is alayout of the mask pattern and determining a transmittance T of thephase shifter, generating a plurality of divided patterns by dividingthe pattern layout, calculating a light intensity Ic generated in alight-shielded image formation region corresponding to each of thedivided patterns on an exposed material by the exposure lighttransmitted through the photomask when a light-shielding film isdisposed in the entire pattern layout, calculating a light intensity Iogenerated in the light-shielded image formation region by the exposurelight transmitted through the photomask when an opening is provided in adivided pattern in which the corresponding light intensity Ic is lagerthan a predetermined value of the divided patterns, and alight-shielding film is provided entirely in a portion other than thatportion in the photomask, and providing the phase shifter in a dividedpattern in which Ic/Io≧T/4 is satisfied of the divided patterns, andproviding a light-shielding portion in a divided pattern in whichT/4>Ic/Io is satisfied of the divided patterns.
 53. The method fordesigning a mask pattern according to claim 52, wherein thelight-shielding film or the light-shielding portion provided in thepattern layout has a transmittance of 15% or less with respect to theexposure light and generates a phase difference of (−30+360×n) degreesor more and (30+360×n) degrees or less, where n=an integer, with respectto the exposure light between the light-shielding film or thelight-shielding portion and the light-transmitting portion.
 54. A methodfor designing a mask pattern for forming a photomask comprising a maskpattern having light-shielding properties with respect to exposure lightprovided on a transparent substrate having light-transmitting propertieswith respect to the exposure light, wherein the mask pattern has a phaseshifter that generates a phase difference of (150+360×n) degrees or moreand (210+360×n) degrees or less, where n=an integer, with respect to theexposure light between the phase shifter and a light-transmittingportion in which the mask pattern is not formed on the transparentsubstrate, the method comprising: creating a pattern layout that is alayout of the mask pattern and determining a transmittance T of thephase shifter, calculating a maximum width Lmax at which alight-shielding effect of the phase shifter with respect to the exposurelight is higher than that of a light-shielding film, and providing alight-shielding portion in a partial pattern whose width is larger thanLmax in the pattern layout, and providing the phase shifter in a partialpattern whose width is Lmax or less in the pattern layout.
 55. Themethod for designing a mask pattern according to claim 54, wherein thelight-shielding film or the light-shielding portion provided in thepattern layout has a transmittance of 15% or less with respect to theexposure light and generates a phase difference of (−30+360×n) degreesor more and (30+360×n) degrees or less, where n=an integer, with respectto the exposure light between the light-shielding film or thelight-shielding portion and the light-transmitting portion.
 56. A methodfor designing a mask pattern for forming a photomask comprising a maskpattern having light-shielding properties with respect to exposure lightprovided on a transparent substrate having light-transmitting propertieswith respect to the exposure light, wherein the mask pattern has a phaseshifter that generates a phase difference of (150+360×n) degrees or moreand (210+360×n) degrees or less, where n=an integer, with respect to theexposure light between the phase shifter and a light-transmittingportion in which the mask pattern is not formed on the transparentsubstrate, the method comprising: creating a pattern layout that is alayout of the mask pattern and determining two kinds of transmittancesT1 and T2 (where T1>T2) of the phase shifter, generating a plurality ofdivided patterns by dividing the pattern layout, calculating a lightintensity Ic generated in a light-shielded image formation regioncorresponding to each of the divided patterns on an exposed material bythe exposure light transmitted through the photomask when alight-shielding film is disposed in the entire pattern layout,calculating a light intensity lo generated in the light-shielded imageformation region by the exposure light transmitted through the photomaskwhen an opening is provided in a divided pattern in which thecorresponding light intensity Ic is lager than a predetermined value ofthe divided patterns, and a light-shielding film is provided entirely ina portion other than that portion in the photomask, providing the phaseshifter in a divided pattern in which Ic/Io≧T2/4 is satisfied of thedivided patterns, and providing a light-shielding portion in a dividedpattern in which T2/4>Ic/Io is satisfied of the divided patterns, andsetting a transmittance of the phase shifter in a divided pattern inwhich Ic/Io>(T1 ^(0.5)+T2 ^(0.5))×(T1 ^(0.5)+T2 ^(0.5)) is satisfied ofthe divided patterns where the phase shifters are provided to be T1, andsetting a transmittance of the phase shifter in a divided pattern inwhich Ic/Io≦(T1 ^(0.5)+T2 ^(0.5))×(T1 ^(0.5)+T2 ^(0.5)) is satisfied ofthe divided patterns where the phase shifters are provided to be T2. 57.The method for designing a mask pattern according to claim 56, whereinthe light-shielding film or the light-shielding portion provided in thepattern layout has a transmittance of 15% or less with respect to theexposure light and generates a phase difference of (−30+360×n) degreesor more and (30+360×n) degrees or less, where n=an integer, with respectto the exposure light between the light-shielding film or thelight-shielding portion and the light-transmitting portion.